introduction-to-programming-in-visual-basic-6-01.pdf

Gary Haggard; Wade Hutchison; Christy Shibata
Introduction: Visual BASIC 6.0
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Gary Haggard, Wade Hutchison & Christy Shibata

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© 2013 Gary Haggard, Wade Hutchison & Christy Shibata & bookboon.com
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4
Contents
Contents
Introduction 10
1 Getting Started 12
1.1 Procedure For Starting 20
1.2 Printing the Program 22
1.3 Saving the Program 23
1.4 Reloading a Program 24
1.5 Exiting BASIC 25
1.6 Loading .txt Files 26
2 Screen Output 27
2.1 Programming Practices and Conventions 27
2.2 The REM Statement 28
2.3 The CLS Command 31
2.4 The Print Command 32
2.5 Print with a Semicolon 33
2.6 Print with a Comma 34
2.7 On Your Own 36
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Contents
2.8 On Your Own 37
2.9 Positioning Output on the Screen 38
2.10 Summary 41
2.11 Putting It All Together 41
3 Input Values and Output Displays 44
3.1 Data Type Values 45
3.2 Variables 45
3.3 Assignment Statements 47
3.4 Dialog Boxes 49
3.5 Displaying Values 51
3.6 Numeric Values As Input 53
3.7 Creating Output Menus 54
4 Numeric Calculations 58
4.1 Operations, Functions and Expressions 58
4.2 Operation Hierarchy 59
4.3 Subexpressions 61
4.4 Built In Functions 63
4.5 Concatenation 67
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6
Contents
4.6 Formatting Output 68
5 Decision Making 75
5.1 Simple Comparisons 75
5.2 Numeric Comparisons 76
5.3 Strings 78
5.4 Character Representation 78
5.5 Dictionary Ordering 79
6.6 String Comparisons 82
6.7 Conditional Statements 83
5.8 Simple If Blocks 83
5.9 The Else Option 85
5.10 Compound Conditional If Blocks 88
5.11 Multi-case If Blocks 93
6 Branching 101
6.1 Line Labels 101
6.2 Unconditional Branching 102
6.3 Repetition of Code 105
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Contents
6.4 Conditional Branching 106
6.5 Repetition a Number of Times 109
6.6 Sentinels 110
6.7 Prompt and Echo 113
6.8 User Interrogation Technique 118
7 For .. Next Loops 121
7.1 The For .. Next Loop 121
7.2 The Step Parameter 128
7.3 Program Applications 132
7.4 Generalized Functionality 137
7.5 Nested Loops 138
8 Random Numbers 142
8.1 The Rnd Function 142
8.2 Using Randomize 144
8.3 Coin Tossing 146
8.4 Tossing a Biased Coin 148
8.5 Die Rolling 150

8
Contents
8.6 Scaling the Rnd Function 153
8.7 A Simulation 158
9 Graphics 163
9.1 Resolution and Color 163
9.2 Coloring Pixels 165
9.3 Drawing Lines 169
9.4 Using the PSet Command 172
9.5 Using the Line Command 175
9.6 Drawing Rectangles 177
9.7 Drawing Circles 182
9.8 Drawing Arcs 184
9.9 Drawing Sectors 188
9.10 Drawing Ellipses 189
9.11 Fill Styles 190
9.12 A Pie Chart 193
9.13 Histograms 195
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Contents
10 Arrays and Tables 199
10.1 Defining an Array 200
10.2 The Syntax of Defining Arrays 202
10.3 Assigning and Using Values in an Array 202
10.4 Finding the Average and the Standard Deviation 205
10.5 File Input 206
10.6 Using Arrays – Searching an Array 209
10.7 Using Arrays – Finding a Smallest Element in an Array 209
10.8 Using Arrays – Interchanging Two Elements in an Array 210
10.9 Using Arrays – Sorting an Array 212
10.10 Using Arrays – Finding a Distribution of Elements 215
10.11 Using Arrays – Parallel Arrays 217
10.12 Using Arrays – Drawing A Pie Chart 218
10.13 Using Arrays – Drawing a Histogram 220
Index 223
Endnotes 227

10
Introduction
Introduction
BASIC has come a long way from the teletype interface1
most current computer users might see in a
museum. The language has evolved into an object oriented programming language used in sophisticated
applications for PCs. Fortunately, BASIC can still be used to help the nonprogrammer understand what
capabilities a programming language has and how all these features are used to solve real problems.
This text is intended to help the student who expects their computer usage to consist primarily of using
word processors, spreadsheets, presentation packages, and other software for specialized applications to
understand what the commands these applications provide with single words and single mouse clicks
are actually doing as encapsulated programs.
The text is organized to introduce problem solving with BASIC in a variety of contexts. Chapter 1 gives
the needed instructions about how to execute a BASIC program with a minimal discussion of technical
systems level ideas. The book uses a template that can be stored as a word processing file and pasted
on the code form to provide all the support needed to write and print out both programs and program
results. Output of computing results is controlled by a simple double click anyplace on the output form.
Using the convenience of storing BASIC programs as word processing files avoids the complications of
saving projects and forms that would never be very meaningful to this audience. Using simple highlight-
copy-paste procedures is all that is needed to start programming. The same process starting with the
code form provides an easy way to save programs for future use. All the procedures used to execute a
program are shown with screen captures that guide the user through the systems set up for programming.
Chapters 2–5 take a step by step approach to introduce the output form and how the user controls the
placement of output. Then variables and assignment statements are introduced to introduce how the
programmer interacts with the computer’s memory. Arithmetic operations are next with a discussion
of the priority of operations as a guide to how the computer operates. Finally, the logical power of the
programming language to ask questions about data and redirect the execution of the program depending
on the current state of a computation introduce the fundamental tools of computing.
Chapters 6–7 provide several ways to process multiple pieces of data using the same code over and over.
Sentinels and data counts are seen as ways to process unknown numbers of data items with conditional
transfers providing a method of ending when the data ends. Once the problem is understood and students
practice with the implementation, the power and simplicity of for loops is understood for what it is, an
encapsulation of code for controlling repetition.
Chapter 8 introduces random numbers. Simulations of simple dice throwing and slot machine plays lay
the groundwork for simple simulations. Scaling of random numbers is also introduced as an important
technique for simplifying parts of simulations.

11
Introduction
Chapter 9 introduces computer graphics. The drawing of a line segment is developed from the two point
formula for a line so readers will see how other functions can be used to draw parts of more complex
pictures. The encapsulated code for Line and Circle are explored in detail as well as how to use color
and drawing styles inside closed figures. The standard spreadsheet charts for pie charts and histograms
are drawn using BASIC and its graphic features.
Chapter 10 introduces arrays and the important idea of file input in BASIC. File input is used so that
applications that reuse data in a computation that depends on an earlier computation using the same
data can be introduced. The obvious examples are finding the mean and standard deviation of a set of
numbers and then asking how many are in a certain range that depends on these two values. Arrays
allow a simplification and generalization of code for drawing pie charts and histograms.
The text provides an introduction to programming (without multiple communicating programs) that
do give an insight into how functions in spreadsheets, for example, are working in back of the interface
consisting of just the name of the function and a list of its arguments.
Each chapter has several features aimed at helping the learning process. The On Your Own sections
are short answer questions to help ensure the material presented is understood. The SYNTAX boxes
are a way to highlight the syntactical aspects that need to be adhered to in any program. Putting It All
Together is a collection of problems that uses the features introduced in the chapter as well as ideas
from previous chapters.
Special thanks to Julia Buffinton for her help with the development and editing of the manuscript.
The authors are interested in helping make this text an effective learning resource. Any errors you find
that you relate to us would be greatly appreciated. Any suggestions for making the text better for your
purposes would also be appreciated and seriously considered. Just send your ideas or questions via email
to vbprogramming@bucknell.edu. All suggestions will be acknowledged and noted at https://www.linux.
bucknell.edu/~vbprogramming.
Gary Haggard
Wade Hutchison
Christy Shibata

12
Getting Started
1 Getting Started
Visual BASIC 6.0 is a powerful object oriented programming language. In this manual, we focus on a small
subset of BASIC (shorthand for Visual BASIC 6.0 from here on) features to learn how to write programs
that illustrate some important application such as simulations, computer graphics, and file processing.
When BASIC is opened, you see the screen shown in Figure 1-1. Click Open and you will see the window
for writing programs.
Figure1-1
BASIC will provide two windows for programming. The first window is used to write the code of the
program. The second window is called a form that is used to display the output when the program is run.
When we choose Open with Standard.EXE highlighted we see the two windows as shown in Figure 1-2.
The problem at this point is that these are just templates for our use and not windows in which we can
actually write code or display output.
Figure 1-2

13
Getting Started
The window labeled Project1 will be used for writing code once we can activate it. The Form1 window
will contain the output from your program. In order to enter programming code, we need to tell BASIC
we want the code writing window to be displayed. The first step in getting the code writing window
made available is to pull down the View Menu on the menu bar as seen in Figure 1-3.
Figure 1-3
By clicking on Code we cause the window labeled Project1 – Form1 (Code) (see Figure 1-4) to be
displayed in front of the other two windows. The two windows in the background will not be used.
Figure 1-4
The form or window used to write code needs to have its associated output form activated so that when
a program is run, there is a form on which to display the output. Activating the output form is a two
step process. First we pull down the menu in which (General) is shown and highlight the second option
Form as shown in Figure 1-5.

14
Getting Started
Figure 1-5
When we click on Form two lines of code will appear on the code window. Load will appear in the
second pull down menu as seen in Figure 1-6. Unfortunately, this is not the option in the second menu
that we actually need.
Figure 1-6
Pull down the menu on the right and find the option Activate and highlight it as shown in Figure 1-7.

15
Getting Started
Figure 1-7
When Activate is chosen (see Figure 1-8), we see two more lines of code appear in the code window.
This code will allow us to write and execute programs.
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16
Getting Started
Figure 1-8
You should just write the line:
Print 3
As shown in Figure 19. This is the code needed to print the number 3 on the output screen. We do not
have to understand the code at this time as we are simply trying to show what happens at this point and
give some motivation for additional code that we will add to all our programs to make the output standard.
Figure 1-9
To execute a program point the cursor at the small filled in triangle that seems to be standing on its
side (see Figure 1-10). You will see a message that says Start appear. If you click on that triangle, the
program will run.

17
Getting Started

Figure 1-10
The output will be displayed in Form1 as shown in Figure 111. The problem is that the current size of
Form1 is too small for the programs we are going to write. Consequently, we need to add a line of code
to the Activate code that will standardize the output form to have room for 25 lines consisting of 80
print positions each.
Figure 1-11
Before we can add new code to the Activate code, we need to end the current program’s execution. We
do this by clicking on the X shown in the red box in Form1 (see Figure 1-12).

18
Getting Started

Figure 1-12
In Figure 1-13 you see the additional lines of code needed to standardize the output form. We need to
identify the font for writing on the output form as well as its size so we get 25 lines and 80 print positions
per line on the output form.

19
Getting Started
Figure 1-13
Now when you run the program, the output form appears as in Figure 1-14.
Figure 1-14
One last problem to resolve and all the technical system level detail will be over and done. At this point
programs can execute and display output on the output form but we have no way to output the results
to a printer. We need to add the following line of code after the End Sub code that is associated with
Activate:
Private Sub Form_DblClick( ) : PrintForm : End Sub

20
Getting Started
This line of code sets up communication between your program and the printer available in your system.
The code should appear as in Figure 1-15.
Figure 1-15
The last detail is how we tell the output form that we want its contents printed. This is simply done
by double clicking the cursor anyplace on the output form that we see when we run the program (see
Figure 1-16).

Figure 1-16
1.1 Procedure For Starting
The development of a code template should help you understand what the special code is all about. In
practice the way to start a BASIC program is to carry out the first three steps shown in Figures 1-1, 1-2,
and 1-3 to see the screen shown in Figure 1-17.

21
Getting Started
Figure 1-17
Now simply write and save the following code in a word processor so you can copy and paste it to the
code form whenever you want to write a program. The code is:
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Getting Started
Private Sub Form_Activate()
Form1.Height = 7000: Form1.Width = 11610: ScaleHeight = 425: ScaleWidth = 728
Font.Name = “Courier New”: FontSize = 11.25: BackColor = vbWhite :AutoRedraw = True
Const font_height = 17 ‘height of font
Const font_width = 9 ‘width of font
‘Start your code here
‘End your code above this line
End Sub
Private Sub Form_DblClick(): PrintForm: End Sub
When BASIC interprets these lines as real code you will see that BASIC has drawn a line between the
End Sub and the Private Sub Form_DblClick(). This indicates the separation between the two different
blocks of code. You should save this code to use every time you write a BASIC program. All programming
will involve entering BASIC commands in the area between “Start your code here” and “End your code
above this line.”
1.2 Printing the Program
Part of the programming process involves printing out a copy of the code that was written. The printed
copy can be taken away from the computer and studied or modified or used to communicate to other
programmers what the program does. What is wanted is a printed copy of the code form. To print a
copy of the program you first pull down the File menu and select Print as shown in Figure 1-18 (a). A
dialog box will appear on the screen as shown in Figure 1-18 (b). In the dialog box be sure the Code
option is selected and then click on OK. A copy of the program will then be printed.

D E
Figure 1-18

23
Getting Started
1.3 Saving the Program
When you are finished or partially finished with a programming assignment, you may want to save the
code so that you can start again at that point of the programming process. The easiest procedure to
use is just to copy the code in the code window and paste it into a word processor and save it. Trying
to save a BASIC program in BASIC involves dealing with both the code window and the output form.
The complications involved in some aspects of the object oriented nature of BASIC are not necessary
for the kinds of programs you learn to write in this book. It is easy to cut and past the code into a word
processor document – a program that you are probably familiar with using. When you want to start up
the program again, you just reverse the procedure by copying the code from the word processor and
pasting it into the code window.
Saving the code in a word processor involves first putting the code on Windows’ Clipboard. The first
step shown in Figure 1-19 (a) is to pull down the Edit menu and click on Select All. When the code is
selected, pull down the Edit menu again and click on Copy (see Figure 1-19 (b)). The code is now on
the Clipboard and ready to be pasted into a word processor.

D E
Figure 1-19
You should now open a word processor (we show Word here but any will be similar) and choose the
Paste option as shown in Figure 1-20 (a). The program file you copied from the code form will now
appear in the word processor as shown in Figure 1-20 (b). You must now save the file in your file system.

24
Getting Started

D E
Figure 1-20
1.4 Reloading a Program
The process of reloading a program for another run or more editing starts by loading the program file
into the word processor. The first step is to choose the Select All option for the file as shown in Figure
1-21 (a). Once the file is selected you need to click the Copy icon near the left side of the Home ribbon
as shown in Figure 1-21 (b). The file is now on the Clipboard and can be pasted into the code form.
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Getting Started

D E
Figure 1-21
Next you open the Code form in BASIC and pull down the Edit menu to choose the Paste option as
shown in Figure 1-22 (a). The program will then be pasted into the code window and you are ready to
operate on the program. See Figure 1-22 (b).

D E
Figure 1-22
1.5 Exiting BASIC
The process to end a session using BASIC involves two steps. The first step shown in Figure 1-23 (a)
involves pulling down the File menu and choosing the Exit option. Before BASIC quits it puts up a
dialog box asking if you want to save the code form and the output form as shown in Figure 1-23 (b).
Just click No and the programs ends.

26
Getting Started

(a) (b)
Figure 1-23
1.6 Loading .txt Files
The procedure for saving the code you write for later use can be slightly adjusted so that reloading it
can be simplified. If the program is saved as plain text using the .txt file type, there are menu choices in
BASIC itself for loading such a file. The procedure starts by choosing the Edit menu and then selecting
the option: Insert file … . You can browse your file system to find the file you want to load. When you
Open the file, it is pasted into the code window.
Unfortunately, you cannot save text in the code window having type txt. However, if you do save the
template as a plain text file, you can load it directly using this option instead of going through the word
processor as described earlier in this chapter. Just be sure the single and double quote marks are the ones
BASIC uses (to the right of L on the keyboard) in any txt file you intend to load this way.

27
Screen Output
2 Screen Output
Every program must provide the user or customer with a clear understanding of the results or information
generated. The main tool for interacting with the user is a special form used to display the results. How
the results are displayed is up to the programmer to decide and make happen. The objective of Chapter 2
is to learn how to control the look-and-feel of the output, i.e., how to use white space and how to position
information. For example, suppose you need to display the graduation numbers for men and women
students over a three year time span. The output could be displayed as shown in Figure 2.1.

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Figure 2-1: Graduation Statistics
Good programming practices and the essential commands and structures used in BASIC to display
information are explained in this chapter. By the end of the chapter, you should be able to write programs
that control the placement of information displayed on the screen.
2.1 Programming Practices and Conventions
Computer programs are made up of instructions to the machine. In all programming languages, the
programming code communicates the step by step actions that are to be performed. Since a computer
can only do what it is instructed to do, the programmer must develop an algorithm or procedure for
the machine to follow. Only after designing the algorithm can a programmer begin to write the code of
a computer program to implement the solution. The rules for writing correct statements for BASIC to
execute is called the syntax of the programming language. BASIC reserves a number of words to help
direct the implementation and execution of the program. These special words like Private, Sub, Print,
and Const are called keywords.

28
Screen Output
In BASIC and all computer programming languages, a program should be easy for both programmers
and users to understand. The program logic embedded in the code written needs to be easily understood
by a programmer. It is not enough for only the original programmer to be able to understand the code.
Other programmers should also be able to understand the code since most programs eventually need
modification that is usually not carried out by the code’s original programmer. On the other hand, it is
equally important that the output produced should be presented clearly and precisely. Users do not want
to find it hard to understand what a program’s output is all about. Well-written programs themselves are
not enough to qualify for a good interface between a computer program and its users, the programmer
needs to use a clear and friendly approach in displaying the results of a program in order to fulfill the
goals of good computer programming.
2.2 The REM Statement
When you read the lines of a program, you should be able to figure out what the program is doing (or
will eventually do) without understanding all the code. (See Figure 2-2. The letters A–F on the left are
not part of BASIC but just the way lines of code can be identified when a program is explained.)
A Rem Prints text on the screen that will be
B Rem expanded later to generate a student’s
C Rem grade average
D Rem OUTPUT: Text on the screen
E Cls
F Print “A Grader’s Entry:”
Figure 2-2: An Example Program
In the program in Figure 2-2, lines A through D tell us what the program will do. This important aspect
of programming is called commenting. Comment statements tell someone reading the program what
the program will do without requiring the person to read the actual code of the program. Comment
statements in a program are non-executable; they are skipped over when the program is run. Comments
serve as messages to the programmer and any subsequent programmer who must deal with the code by
indicating what is happening in the program. If all the commands of a program directing the computer
to do something were deleted, the comments should still give a clear outline of the program’s structure.
Always use commenting in your programming so that you and others reading your programs will be
able to follow and understand what is happening.

29
Screen Output
In BASIC, commenting is done using the Rem statement (“Rem” is short for “remark.”). Since comment
lines are not executable, any combination of text may follow a Rem statement. As an example, line D
of the program in Figure 2-2 is a comment indicating that the executable code in this program displays
text on the screen as output:
D Rem OUTPUT: Text on the screen
The only syntactic restriction on comments is that each line of a comment must start with the keyword
Rem. There are certain coding conventions we follow when commenting. These conventions help
provide for a uniform program structure. Notice in Figure 2-2 how all the Rem statements are at the left
margin. Notice also how the executable statements (E and F) line up. Besides these spacing or indenting
conventions, the first comment gives a description of what the program does or what problem it solves.
Each line of a comment must begin with Rem as seen in A–D. Typically, after the comment explaining
what the program does, we use a comment beginning with the word:
INPUT:
to specify what data is needed for the execution of the program. In the example program, no data is
needed so this remark is omitted. We use the word

30
Screen Output
OUTPUT:
tospecifywhatinformationresultsfromtheexecutionoftheprogram.ExaminetheprograminFigure2-3
to see how these commenting conventions are incorporated in a program. (For now, do not worry about
the code used to produce the input and output for the program in Figure 2-3.) Rem statements can
appear any place in a program. Often Rem statements are used to indicate what task is performed by a
group of statements. Just the Rem statements in a program should provide an outline of what and how
the program accomplishes a task.
Rem Prompts a user for any word and then
Rem prints that word on the screen
Rem INPUT: A word entered by the user
Rem OUTPUT: Input word on the screen
A Cls
B Rem Get input
C word = InputBox (“Type any word”)
D Rem Display output
E Print word
Figure 2-3: Program Demonstrating Commenting Conventions
SYNTAX
Rem Statement
Rem is a keyword that begins a non-executable statement in a program. Rem
may be followed by any message to the programmer or about the program. A
Rem statement is ignored at execution time. Rem occurs at the start of a line in a
program.
Notice that comments B and D give an outline of the program’s logic even if lines A, C and E are not
well understood yet. As an alternative to starting a line of a program with Rem, you can enter a single
quote mark at the beginning of the line or anyplace following the statement on the line to indicate the
start of a comment.

31
Screen Output
2.3 The CLS Command
In addition to creating programs that are understandable to the programmer, you should write programs
that produce output that is understandable to the user. A screen with the number like 42 appearing on
the output form after a program is executed will usually leave the user wondering what it means. One
command used to help produce clear output is the Cls command. (“Cls” stands for “clear screen.”) Cls
is usually used at the beginning of a program as well as after the entering of data and before output
is displayed. When executed, the Cls command clears the display area of the output form so that the
output produced will be displayed on a blank form. After the Cls command is executed, the next output
will be positioned at the upper left corner of the display area. Cls is a keyword and may only be used
as described here.
In the program in Figure 2-4, we execute a Cls command before the output is displayed so that the
output will be displayed on a blank output form. (See Figure 2-4.) Each time the program is executed,
the form is cleared before any output is displayed.
Rem Displays three lines of text Line 1
Rem on the screen. The lines are Line 2
Rem labeled from 1 to 3. Line 3
Rem OUTPUT: text on the screen
Cls
Print “Line 1”
Print “Line 2”
Print “Line 3”
Program Output
Figure 2-4 – The Program with Cls and the Output
SYNTAX
Cls Command
Cls is a command that causes the output form to be
erased and the print head to be placed at the top left
corner of the output form screen.

32
Screen Output
2.4 The Print Command
The Print command displays either text or numeric values on the output form. A text message following
a Print command must be enclosed in double quotes. We call text in double quotes symbolic constants.
(This notion will be defined more carefully later, for now just think of putting an English word in quote
marks.) The text message will then be displayed just as it appears within the double quotes. If you want
to display a numeric value, no double quotes are used. The Print command with no output indicated
has the effect of skipping a line on the output form because the end of the Print command has a
hidden character that causes a carriage return action by the printer. You can use this idea to put lines
between parts of a program’s output. Examples of the Print command are given below:
Print “dog”
Print 12
Print
The output of the first Print statement is simply the word dog without the double quotes around it. The
double quotes simply tell BASIC that what is between the double quotes is a string of symbols. The second
print command displays the number 12 on a new line and the third print command simply advances
the print position to the beginning of the fourth line without printing anything.
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33
Screen Output
2.5 Print with a Semicolon
With judicious use of the Print statement for spacing lines, we can control the line placement of text. To
display the numbers 100, 200, and 300 one after another on a single line, we need another mechanism.
BASIC uses semicolons and commas to position output within a line. For example, if we use the following
Print statements:
Print 100
Print 200
Print 300
we will get the following output on three different lines:
100
200
300
However, if we place a semicolon at the end of the first two Print statements as follows,
Print 100;
Print 200;
Print 300
we will get the following output:
100 200 300
AsemicolonfollowingtextindoublequotesoranumericvalueinaPrintstatementcausesthenextoutput
of numbers and/or text to be displayed on the same line starting at the next available print position. For
text items there is no space between successive pieces of text. For numeric values a space appears because
BASIC wants to be able to put a sign before a number if it is needed. Rather than implementing three
separate Print statements, as used above, we can produce the same output by using one Print statement
with semicolons between the items:
Print 100; 200; 300
This output of this Print statement is again:
100 200 300

34
Screen Output
2.6 Print with a Comma
In the BASIC output form, the font and the window size have been organized so that there are 25 rows
each consisting of 80 positions across. Each position on a line can hold one character-a letter of the
alphabet, a numeral, or a special character. Each row is subdivided into zones that contain 14 positions
each (see Figure 2-5).
0 14 28 42 56 70
Zone 1 Zone 2 Zone 3 Zone 4 Zone 5 Zone 6
Figure 2-5 – Print Zones
There is a syntax option in the Print statement that lets us use this line organization. For printing a list
of values, a comma following a value in the list causes the print mechanism to advance to the next empty
print zone before printing the next value. For example, the Print statement:
Print 100, 200, 300
will produce the following output:
100 200 300
Each item is displayed at the left boundary of a separate print zone.
When text messages are printed, the message may be too long to fit into a single print zone. A long
message will be printed completely and the comma in the Print command following the message signifies
that the next piece of information should appear at the start of the next empty print zone.
The following are examples of valid Print commands: (There will be four lines of output.)
Print 34
Print,
Print “Number”;
Print 34, “Jerry”;
Print 56, 90; 24, 67
Print “Gross”, “Net”
Print

35
Screen Output
When a comma appears at the end of a Print statement as in
Print 35, 25,
the next Print statement encountered in the execution of the program will have its first value displayed
in the next empty print zone on the line used for printing 35 and 25. If the Print statement ends with
a semicolon, as in
Print 35, 25;
the next element printed by the program will appear beginning in the next print position on the line
on which 35 and 25 were printed.
SYNTAX
Print Command
Print list of elements to print
Elements of the list are separated from each other using commas
and semicolons. A comma causes the print head to move to the
next empty print zone and the “;”causes the print head to move to
the next print position.
EXAMPLE: Print 3, “ABC”; 5
3 ABC5
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36
Screen Output
2.7 On Your Own
1. Enter and execute the following three-line programs that demonstrate the use of commas
and semicolons in a Print command.
a) Print 100, b) Print 100; c) Print 100
Print 200, Print 200; Print “Text”
Print 300 Print 300 Print 300
When using the Print command to display several items, it is a good idea to include punctuation. If
you forget to include punctuation such as a comma or a semicolon, BASIC will automatically include a
semicolon. Thus, if you forget to include punctuation between items, a semicolon will be put in for you,
and the items will be displayed one after the other on the same line.
ThevariationsofthePrintcommandthathavebeenexplainedareparticularlyhelpfulinproducingtables.
Example 2-1. Produce a table that shows the graduation numbers of males and females at a university
for the years 1970, 1980, and 1990.
SOLUTION: The output required is the table:
1970 1980 1990
Male 476 470 490
Female 364 465 560
----- ---- ----
Total 840 935 1050

37
Screen Output
The code that will produce this table is:
Rem Produce a table that shows the number of
Rem males and females who graduated in 1970,
Rem 1980, and 1990.
Rem OUTPUT: Table with information
Cls
Rem Display output
A Print , 1970, 1980, 1990
B Print
C Print “Male”, 476, 470, 490
Print “Female”, 364, 465, 560
Print , “----”, “----”, “----”
Print “Total”, 840, 935, 1050
The program uses commas between items in a Print statement to display certain items in consecutive
print zones on a single line. Since each piece of output information fits in a print zone, the effect of the
Print statements with commas between elements is to make the output appear in tabular form. Notice
that in line A, there is a comma appearing before any information to print. This comma causes 1970 to
be printed in print zone 2. Here B causes a blank line to appear between the dates and the first set of
numbers. In line C the program needs to print “Male” in print zone 1 and so the string is listed and then
followed by a comma so that the first numeric value is printed in print zone 2 as required.
2.8 On Your Own
1. Write a program to produce the following table that gives information about three states.
The area is given in square miles.
State Capital Population Area
Alaska Juneau 570000 570374
New York Albany 18058000 47224
Texas Austin 17349000 261914
Do not output the lines surrounding the table.

38
Screen Output
2.9 Positioning Output on the Screen
Though we have been concerned with the placement of text in a line, we have not concerned ourselves
with any special placement of the text on the output display. The first output of a program has always
been displayed beginning in the default position in the upper left corner of the display. For variation in
output displays, programs can position output at a specific place on the display form.
The output form can be thought of as a grid composed of 25 rows each with 80 columns. The rows
are numbered from 0 to 24 and the columns are numbered from 0 to 79. Before each Print command
BASIC must know on what line and in what column on that line the printing should begin. The variables
CurrentX and CurrentY are the variables (a formal definition comes later, for now just assume BASIC
uses these names to keep track of some information it needs) used to know how to position the print
head. BASIC uses CurrentY to hold the number of the row and CurrentX the column in that row
where printing should begin. When a Print command is finished executing CurrentX and CurrentY are
given values so that the next print command will start at the left margin of the next line of the output
form. When a program begins to execute, BASIC sets both CurrentX and CurrentY to zero indicating
that printing will start at the top left position of the output form. CurrentX is the distance from the left
side of the display. CurrentY is the distance from the top of the display. A program may override the
automatic positioning of the print head and explicitly change the values of CurrentX and CurrentY to
control the location of the next piece of output on the display. The computer measures horizontal and
vertical distance on a screen in terms of pixels (the smallest resolution unit on a display device). Rather
than think in terms of pixels that are too small to hold a symbol we can see, we have organized the
screen to consist of lines that have a fixed height in terms of the number of pixels and such that each
print position in a line has a fixed width in terms of the number of pixels. Each row is set to be 17 pixels
high and each column is 9 pixels wide. These dimensioning values are chosen so that one character of
the font used for output will fit in a box of this size. (See Figure 2-6 for the code in the code template
that defines this “box” size.)
Const font_height = 17 ‘ height of font
Const font_width = 9 ‘ width of font
Figure 2-6: Constants for Converting to Pixels
To print beginning at row 19 and column 56, change the values of CurrentX and CurrentY before
printing as shown in Figure 2-7.
CurrentY = 19 * font_height
CurrentX = 56 * font_width
Print “Over here!”
Figure 2-7: Example of Positioning Output

39
Screen Output
The output is printed in row 19. The letter “O” is printed in column 56, “v” is in column 57, and so on.
(The equal sign is used to set the value of CurrentX and CurrentY.) CurrentY is set to 19 times the
height of a single line and CurrentX is set to 56 times the width of a single print location. Now when
the print command is ready to execute it will first move the print head to the position on the output
form represented by the current values of CurrentX and CurrentY.
To demonstrate the effect of changing the values of CurrentX and CurrentY, we will show the output
of programs that do and do not change these values. First, refer to Figure 2-8 which shows the output
of a program that does not change the values of CurrentX and CurrentY.
Rem Prints text on the screen that will be
Rem expanded later to generate a student’s
Rem grade average.
Cls
Rem Display output
Print “A Grade Calculation:”
A Grade Calculation:
Figure 2-8: Program that Uses Default Positioning for Output

40
Screen Output
We now change the values of CurrentX and CurrentY before the Print statement in the above program
to change the position of the output text. (See Figure 2-9.)
Rem Prints text on the screen that will be
Rem expanded later to generate a student’s
Rem grade average.
Cls
Rem Set output location to be row 4 and column 15
Rem Display output
Print “A Grade Calculation:”
A Grade Calculation:
Figure 2-9: Program that Positions Text Output
Notice that in the output of the program in Figure 2-9 the line of text is displayed beginning in column
15 of row four of the display. An important part of programming is to design visually pleasing output
displays that readily convey the important information. We will change the values of CurrentX and
CurrentY to produce clear and concise program output with adequate spacing to make the information
easy to understand.
SYNTAX
CurrentX and CurrentY
Commands used to position the print head on the output form.
The values are given in terms of the pixel structure of the output
screen. The next print command begins at that position.

41
Screen Output
2.10 Summary
In this chapter, we have discussed elementary features of the output command Print. We are interested
in writing programs that effectively present information. By setting the values of the CurrentX and
CurrentY coordinates and using Print and Cls commands, we can position text anywhere on the output
display. With judicious use of these techniques we can even produce simple pictures. We will continue
to focus on using features of BASIC to provide an effective way to present output so that the user readily
understands what information is presented. We are interested in well-designed interfaces between the
user and a program. We call such interfaces user-friendly.
2.11 Putting It All Together
1. Write a Print statement to display your name on the screen. Hint: Figure 2-9 is a very good
model for this problem. Set the values of the CurrentX and CurrentY to determine the
output location. The output location should be near the center of the display. (Recall that the
rows are numbered from 0 to 24 and the columns are numbered from 0 to 79.)
2. Write a program to print your first name at the left margin of line 13 and your last name so
that the last letter is in column 79 of line 21.
3. (a) Write a program that prints your first name using a print statement that ends with a
comma. Then write a second print statement to display your last name.
(b)Repeat part (a) but now use a semicolon at the end of the first print statement.
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42
Screen Output
4. Write a program to produce the following table that shows game results for State U’s
basketball team for the past three years. (This program does not need to change the default
values of CurrentX and CurrentY.)
Year Overall Wins at Wins
Record Home Away
2012 19-9 13 6
2013 21-6 14 7
2014 16-10 11 5
5. Write a program to produce the following table that shows coffee sales at the University’s
snack bar in the library. The table should use print zones 2 through 5 on lines 10 through
15.
COFFEE SALES
DAY SMALL MEDIUM LARGE
Monday 95 68 51
Tuesday 88 72 46
Wednesday 112 83 47
6. Write a program to produce the following table which shows the sales record of each
sales person in a company. (This program does not need to change the default values of
CurrentX and CurrentY.)
Sales Today’s Week Commission
Person Sales Total
Brown 509.85 2367.98 710.39
Jones 366.91 1982.82 594.62
Roberts 430.11 2284.43 685.33
Smith 399.08 1857.68 557.35
7. Write a program to draw a house centered on the display as shown in the figure below..
Hint: The executable part of the program that draws the house consists of commands to set
the values of the CurrentX and CurrentY before each Print command. The center point of
the roof could be printed using
Print “*”

43
Screen Output
The next line of the roof could be printed using:
Print “* *”
There should be three spaces between the pair of “*”s.

/LQH
ROXPQ
/LQH
ROXPQ

44
Input Values and Output Displays
3 Input Values and Output Displays
BASIC programs usually consist of more than just commands to display output. Programs use commands
that cause the user to be asked for some information that the program needs for its execution. Programs
also do arithmetic with values supplied by the user as well as with values created by the program in the
course of its execution. Still other problems require the program to ask questions about a current value
in a storage location to determine what to do next. By the end of this chapter, you should understand
how to write programs that use dialog boxes for input and display menus for output. Since the dialog
boxes and display menus are the interface between the user and the computer, they should be designed
to be effective and user-friendly. Using arithmetic operations and asking questions about values are dealt
with in Chapters 4 and 5, respectively.
A typical application using user supplied information is a sales receipt. The idea is to display all the
information and whatever information is derived from the input values so that the user understands.
The example shown in Figure 3-1 gives order information for nine coffee mugs.
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Figure 3‑1: Sales Information
3.1 Data Type Values
A literal is a value that is either a number, such as 3; or a string of characters such as “the end.” To
distinguish data types we refer to a numeric literal as a numeric value. A string literal is a sequence of
characters enclosed in double quotation marks. We also refer to a string literal as a word or symbolic
constant or string constant.
3.2 Variables
A variable is a user supplied name for a location in computer memory. A variable’s location in memory
can contain a literal such as a number or a string of characters. BASIC takes care of determining what
memory location will be assigned to a variable. BASIC also manages the operations of putting a value
into a storage location and accessing a value from a storage location. BASIC will use the value in a storage
location whenever the variable name that refers to that location occurs in the program.
Programs in this book will deal with two types of data or literals: numeric and string. Numeric data is
simply a whole number or a number that includes a decimal point. String data will be any sequence of
symbols. A variable can represent a storage location for either type of data and BASIC keeps track of
the type of data that a variable represents. You should not use the same variable to store numeric data
at one point in a program and string data at another point. We call a variable that represents a string
value simply a string variable. A variable that represents a numeric value is simply called a numeric
variable. A numeric or string expression is simply a combination of literals, variables, or operations for
a given type of data. Operations for data types will be dealt with in later chapters.
BASIC requires variable names be formed using the rules that are shown in the SYNTAX box.

46
SYNTAX
Variable or Variable Name
A variable name can be up to 255 characters long. A variable name must begin
with a letter of the alphabet and consist of only letters, digits, and underscores. After
the first letter, the rest of the variable name can be any combination of letters, digits
and underscore characters. BASIC keywords cannot be used as variables. Variables
are not enclosed in quotation marks but represent an address of a storage locations
in memory. Variable names are often referred to as a variable.
Keywords like Int, Count, and Name often seem like natural names for variables. If you use a keyword
other than as BASIC intends, you will be given an error message about the line of code containing the
keyword. You may look at the line of code and wonder what is wrong! (If you type a variable name using
lowercase letters and BASIC automatically capitalizes the first letter, this is a strong sign that the name is
a keyword. For this reason, it is suggested that you begin variable names with lowercase letters.) Notice
that neither a hyphen nor a period may be used in forming a variable name.
Variable names should describe the values they represent. The following are examples of valid variable
names that indicate the values they represent:
payment
name1
total_Sales
It is clear that variable names like X and Y do not convey as much information about what the variables
represent as do payment and total_Sales. (You can play games with names and have the name imply
something that is not true as using tax to represent a person’s surname. In the long run you will be better
off using names that infer the value the variable represents.)
On Your Own
1. Explain why the following variable names are invalid:
185CSCI Print
WVBU90.5 #one
zip code Zip-code
Write a corrected version of each of these names.

47
3.3 Assignment Statements
An assignment statement in a programming language is an instruction that assigns a value to a variable,
i.e., tells BASIC to place a value in the storage location associated with the variable. The semantics of
a stqatement is the result of executing the statement-what are we intending to have happen when this
statement is executed. The semantics of an assignment statement is that a value is placed in a storage
location and can be used by referencing the name of the storage location, i.e. the variable name. The
assignment statement consists of a variable name, an equal sign and then an expression or a literal. The
variable name represents the storage location that will hold the value of the expression or literal that
occurs on the right hand side of the equal sign. For instance, the following is an example of an assignment
statement involving a numeric value:
payment = 20
In this assignment statement, payment is the variable name while 20 is the value assigned to the storage
location that payment is assigned by BASIC.
Variables as well as literals can appear on the right side of an assignment statement:
grade1 = 100
grade2 = grade1
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After the execution of these two statements, both grade1 and grade2 will have 100 stored in the memory
locations they are assigned. Variables on the right side of an assignment statement should have previously
been assigned a value so that the assignment of a value to a storage location makes sense. The semantics
of the second assignment statement is to take the value in the storage location grade1 and put a copy
of this value in the storage location represented by grade2. The contents of grade1 is not changed. The
value assigned to a numeric variable may also be a number calculated by a mathematical operation. We
discuss mathematical operations in the next chapter.
In an assignment statement involving a string variable, a character string that is being assigned to a string
variable must be surrounded by double quotes to distinguish it from a variable name. For example, the
following lines are assignments to string variables:
nam = “Mary Kay”
friend = nam
After the execution of these two statements both nam and friend will have the string “Mary Kay” stored
in the memory locations they represent. We first put Mary Kay in the storage location nam (we identify
the name of the storage location with the storage location). Notice that the string “Mary Kay” has eight
characters. The space between y and K is treated as a character just as a comma, a period, or any other
character that the computer recognizes. We are tempted to use Name as the variable name but if we do
we get an error because Name is a keyword.
SYNTAX
Assignment
variable = literal or variable
The left side of an equal sign always has the name of exactly one storage
location. The right hand side generates a value to put in that storage location.
In the next chapter we will explain how more complicated expressions can also be part of an assignment
statement.
On Your Own
1. Explain why the following assignment statements are invalid. Write a corrected version of
each of these statements.
town = “Lewisburg”
num , total = 12
x, y = 3
x = y = 3

49
3.4 Dialog Boxes
A dialog box is a window that appears on the screen to ask the user for a response and then is removed
after the user responds. Dialog boxes allow users to input data to be processed by the program. In most
cases, the computer will “ask” a user for certain data as the program is executing and will wait for the
user to respond before continuing the execution of the program.
In BASIC, the input procedure for data uses the built-in-function InputBox(). The InputBox() function
uses a short message called a prompt to indicate to the user the type of data to provide. The InputBox()
function brings a value into the program that must be stored in some variable. Consequently, we assign
the result of this built-in-function to a variable name just as we saw how to assign any other value to a
variable.
As an example, when the statement
surName = InputBox(“Enter your last name.”)
is executed, a dialog box with the prompt at the top left is displayed on the output form. The dialog box
is shown in Figure 3-2.

3URPSW
(QWHUDYDOXH
Figure 3‑2: BASIC Dialog Box for InputBox
The prompt is shown in the top left corner of the dialog box and indicates to the user what kind of data
to enter in the area pointed to at the bottom. The string entered by the user is assigned to the variable
surName. A string variable can also be used as a prompt:
kindOfInfo = “What’s the frequency of this event (Often/Rare)?”
frequency = InputBox(kindOfInfo)

50
When this code is executed, the message “What’s the frequency of this event (Often/Rare)?” appears as
the prompt message in a dialog box. The data entered by the user is assigned to the variable frequency.
Notice how informative the prompt is in indicating the responses wanted. Without the prompt the user
would not know what to enter.
The syntax of InputBox() is summarized here:
SYNTAX
InputBox()
variable = InputBox(“prompt”)
InputBox() accepts a string of characters entered from the keyboard and stores
them in variable. The prompt string tells the user what kind of information is to
be entered.
EXAMPLE: surName = InputBox(“Enter a surname:”)
In the example, “Enter your surname:” is used as a prompt to tell the user what kind of information is
needed. The prompt is always enclosed in a pair of double quote marks.

51
On Your Own
1. Explain why the following statements are invalid. Write a corrected version of each of these
statements.
zip = InputBox
s = InputBox (Enter your size.)
2. The following statement is syntactically correct, but what is its semantics: X = InputBox()?
3.5 Displaying Values
Variable values can be accessed and displayed by the Print command. The variable name of the storage
location containing the information to be displayed follows the keyword Print. Do not put quotation
marks around the variable name. (What will be printed if you do?) This usage of the Print command
is shown in the following code:
rating = “Poor”
Print rating
When these instructions are executed, the word “Poor” is displayed on the screen.
A text message may also be displayed with values of variables. A semicolon separates the text message
from the variable if the variable value is to be displayed adjacent to the text. If the variable value is to
be placed in the next print zone, a comma is used. (If no punctuation is specified, BASIC automatically
includes a semicolon.) The following code prints text and the value of a variable:
temp = 44.4
Print “It’s”; temp; “degrees outside.”
Run this program and determine what needs to be changed to make the output more readable.
When using a semicolon in a Print command, you may need to supply spaces as part of the string so
the output reads as intended. For example, the two print statements:
Print 35; “degrees”
Print 35; “degrees”
have the following outputs:
35degrees
35 degrees

52
Example 3-1. Using variables and the InputBox() function, write a program that inputs a person’s name,
hometown, and three favorite flavors of spice drops. Display the data entered in the center of the output
display as shown:
Name: Chandler Bing
Hometown: New York
Favorite flavor: Apple
1st runner up: Strawberry
2nd runner up: Lemon
SOLUTION:
Rem Display favorite spice drop flavors
Rem INPUT: Person’s name, hometown, and three favorite spice drop flavors
Rem OUTPUT: Input data centered on the display
Cls
Rem Get input
nam=InputBox(“Name:”)
home=InputBox(“Hometown:”)
flavor1=InputBox(“Favorite space drop flavor #1:”)
flavor2=InputBox(“Favorite spice drop flavor #2:”)
flavor3=InputBox(“Favorite spice drop flavor #3:”)
Rem Display output
CurrentY = 8*font_height : CurrentX = 30 * font_width
Print “Name: “;nam
Print “Hometown: “; home
Print
CurrentX = 30 *font_width
Print “Favorite flavor: “;flavor1
Print “1st Runner Up: “; flavor2
Print “2nd
Runner Up: “;flavor3
COMMENTS: Notice the extra blank spaces included before the closing quote marks in the string
constants in the last two Print commands. These spaces cause the names of the flavors to line up when
they are printed. What would the output look like if the last three print statements had commas in the
place of semicolons? Try it! Also observe that CurrentY is not set again after the first print statement.
We do not need to make any special line settings because the output is to occur on consecutive lines and
CurrentY is always set to a value that moves the print head to the left margin of the next line.

53
On Your Own
1. Write a program to input your name and address as an entry in an address book. Print the
entry in the center of the display using the following format:
Lisa Simpson
742 Evergreen Terrace
Springfield, NT 49007
3.6 Numeric Values As Input
Data entered in a dialog box using the command InputBox() is of type string. BASIC treats the data as
a sequence of characters. Typically programs also use numeric values to carry out calculations. Numeric
values also need to be input when the program is executing. Values used in calculations must be numeric
values, not strings. Data entered in a dialog box for the command InputBox() are brought into the
computer as a string of characters regardless of whether the data is string data or numeric data. If the
value is numeric and will be used in a computation BASIC needs to convert the string to a numeric
representation. The Val() function as described in the SYNTAX box does just that.
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SYNTAX
Val()
variable = Val(“numeric literal”)
where a numerical literal consists of digits and
possibly a decimal point and possibly a sign (+/-)
EXAMPLE: Pi = Val(“3.14159” )
The argument for the Val function is normally the result of the execution of the
InputBox() function as:
There are cases when Val() is forgotten where BASIC does not make the string to numeric representation
conversion and unexpected results may be produced.
On Your Own
1. For the program
X = Val(InputBox(“enter salary”)
Print “salary, X”
What is printed?
2. For the program
X = Val(InputBox(“salary”))
Print Salary = , “X”
What is printed?
3. What will be the output of the following program segment:
X = InputBox(“Enter 1234”)
Y= InputBox(“Enter 4567”)
Print X + Y
3.7 Creating Output Menus
An output menu is a combination of labels and values positioned on the output form to make it easy
for users to view and understand information. In Example 3-1, we saw a program that set the values of
CurrentX and CurrentY and used these settings along with the Print command to create an output
menu. The program in the solution of Example 3-1 is a good example of a program that creates user-
friendly output using an output menu.
Example 3-2. Write a program that inputs earnings information for a surfing instructor and produces
a menu that displays this data as well as the total earnings.

55
OUTPUT: Name: Phoebe Buffay
Number of sessions given: 8
Payment per session: 30
Total tips: 40.25
Total earnings: $280.25
SOLUTION:
Rem Generate an earnings report
Rem INPUT: Name of employee and earnings data:
REM no. of customers and amount of tips
Rem OUTPUT: The input information and earnings data
Cls
Rem Get input-name, no. of customers, and total of tips
nam = InputBox(“Name:”)
num = Val(InputBox(“Number of sessions given:”))
fee = Val(InputBox(“Payment per session:”))
tips = Val(InputBox(“Total tips:”))
Rem Enter total earnings
total = Val(InputBox(“Enter total of all earnings”))
Rem Display output
Print “Name: “; nam
Print “Number of sessions given: “; num
Print “Payment per session: “; fee
Print “Total tips: “; tips
Print “Total earnings: $”; total

56
COMMENTS: The prompts used with the InputBox() commands are clear in describing what values
are to be entered. The prompt is designed as an argument for the InputBox() command so the user
enters the appropriate data. If a user enters an incorrect type of data, the program will use the incorrect
data as if it were correct! Similarly, note that the output labels clearly identify the values printed so that
the results of the program are easily understood. We will learn how to output a value automatically in
a monetary format when we discuss the Format() option in the next chapter.
The Val() function is applied to the result of the InputBox() function only when the program expects
the user to enter a numeric value.
Note that CurrentX is changed more often than CurrentY. After each Print command in this program,
the CurrentX and CurrentY values are automatically set to position the print head at the beginning of
the next line. When we want the next output to appear in this next line, CurrentY is already correctly
set and does not need to be changed. In these cases, only the value of CurrentX needs to be changed to
place the output correctly at a position away from the left edge of the output form.
1. Write a program that accepts as input a dog’s name, breed, and favorite toy. Display this data
in the center of the screen.
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offered to me.”

57
2. Write a program that has a name and the age of the person as input. Display this
information in the middle of lines 18 and 19. The name should appear in line 18 and the age
in line 19.
3. Write a program that has a name and an address (street, city, state, zip) of two different
people as input. Display the information as two columns of output with the columns’ left
margins being locations 6 and 48.
4. Write a program that has a student’s name and social security number as input. Print the
name starting at column 18 of line 9 and the social security number in the middle of the
next line.
5. Input the name of a course and the average grade for each of the three hourly exams.
Display the information in the middle of the output form with the course name on line 10.
The grades should be labeled: Average Exam I:, Average Exam II, and Average Exam III. The
grade labels should start in column 30 of lines 12, 13, and 14.
6. For input enter a student’s name and the four courses the student is enrolled in. Display the
name followed by a blank line followed by each course on a different line. Center all the
output in the center of the output screen.
7. Enter the name of two teams competing against each other and the final score for each
team. Display the information as shown in the middle of the output form.
Team1 vs Team2
xxx xxx
8. Write a program that accepts as input the name of a major league baseball team and its
current won-loss record. Display the information in the center of the output form. Take 32-
19 as the won-loss record.
9. Input the name of a city and the high and low temperatures for one day (enter as name of
month and day of the month). Title each piece of information and display on different lines
starting with line 10. All titles should start in column 25

58
Numeric Calculations
4 Numeric Calculations
Programming involves more than creating effective user interfaces. The programmer must also know
how to process input data (such as number of hours worked and pay rate) to generate results (such as
payroll information). This chapter takes another step in giving you the tools needed to solve problems that
involve computations. Computational problems typically involve a combination of numerical operations
and the use of predefined mathematical functions.

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Figure 4‑1: Sports Statistic Computation
4.1 Operations, Functions and Expressions
BASIC programs often include mathematical operations performed on values input as well as on other
values generated by the program but not directly provided by the user. In BASIC, numerical operations
may be performed on numbers and the values stored in locations representing numeric values. BASIC
numerical operators that act on one or two values are listed in Table 4-1. A command that combines
explicit values, constants, variables, operators, and functions is called an expression. A simple assignment
statement is an expression but in general, expressions will involve more than a single term.
Operator Description
+ Addition
- Subtraction
* Multiplication
/ Division
- Number negation
^ Exponentiation
Table 4‑1: BASIC Numerical Operators

59
4.2 Operation Hierarchy
To evaluate an expression in a program containing only arithmetic operations, there are two issues to be
understood. The first is to know which values will be used in the computation. The second is to know
the order in which the operations will be performed. In an expression involving only operations and
constant values, the operations are performed on the values in the expression. If an expression includes a
variable, the computer must access the current value of the variable and use that value in the computation
in place of the variable name.
The question of how the computer will execute a series of arithmetic operations used in an expression
is a bit more complex. If you are faced with a computation without parentheses such as
-A * B + C / D ^ E – F
there are several possible ways to evaluate the expression. Proceeding from left to right and doing the next
operation is one possibility. Such an approach does not fit the rules we are familiar with for evaluating
expressions. The key idea is to recognize that some operations are more important than others and we
must do the more important operations first. The order of importance or priority for arithmetic operators
is shown in Table 4-2.

60
1st
priority ^ Exponentiation
2nd
priority - Number negation
3rd
priority * / Multiplication and division
4th
priority + - Addition and subtraction
Table 4‑2: Priority of Arithmetic Operations
The operation of changing the sign of a value, called negation, is the only operation to act on a single value.
The negation operator is different than subtraction which operates on two values. Typically, negation
occurs on the first value in an expression or before a parenthesis indicating the result of an expression in
parentheses is to have its sign changed. We do not order operations such as * and / between themselves.
When we are evaluating operations at the same priority level, we evaluate any operation at that level as
it occurs moving from left to right. The rule the computer follows for executing expressions will give the
result you expect. The evaluation process starts by scanning the expression from left to right doing all the
operations involving the highest priority operators that occur in the order they occur. Then the values
calculated are substituted into the expression forming a simpler expression only involving operations
at a lower priority. Now, the computer again proceeds from left to right scanning this intermediate
expression and evaluates operations at the highest priority remaining in the order in which they occur.
The computer continues to scan the resulting simpler expressions in this way until a single value results.
For example, to evaluate the expression 3 * 4 + 5 ^ 2 / 5 – 8, the steps needed are shown in Table 4-3.
3 * 4 + 5 ^ 2 / 5 – 8 Initial expression
3 * 4 + 25 / 5 – 8 After exponentiation
12 + 5 – 8 After multiplication and division
17 – 8 After the addition
9 Final result after the subtraction
Table 4‑3: Example Arithmetic Expressions
The asterisk is used to signify multiplication in BASIC. Just entering
12 num
to multiply the value of num by 12 will give an error. The correct expression is
12 * num or num * 12

61
When variable names are involved in assignment statements involving arithmetic expressions, the
expressionlookslikenormalalgebrabuthasadifferentmeaninginmanycases.Theassignmentstatements
shown in Table 4-4 are valid.
A x = 0
B x = x + 1
C y = x * 2
D total = x + y
Table 4‑4: Assignment Statements
Statement B needs a bit of an explanation. The variable x occurs on both sides of the equal sign. It
looks as if the statement means 0 = 1 which is obviously not true. BASIC takes some liberties with our
normal expectations. Here the equal sign does not mean equality. The language designers had only the
keyboard symbols to use, and they knew that they would need a symbol to represent “assign the value of
an expression to a variable.” What they did was use the equal sign to mean different things in different
contexts. This is called symbol overloading.The equal sign in B means: evaluate the expression on the
right side of the equal sign and store the result in the location of the variable whose name occurs on
the left side of the equal sign. When evaluating an expression, BASIC first sets aside the storage location
on the left side of the equal sign before evaluating the expression on the right side of the equal sign.
Consequently, the expression on the right hand side is evaluated independently of any knowledge about
where the result will be stored. Thus, in expressions like B, the same variable can occur on both sides
of the equal sign without causing any difficulty provided we understand the semantics of the statement.
The meaning in B is to add 1 to the current value of variable x and store the new value at x’s location.
Another meaning of the equal sign is discussed in Chapter 5. Notice also that before and after B is
executed, the storage location x contains different values! A storage location’s value is always the last
value stored at that location with no memory of any value that was previously in that storage location.
4.3 Subexpressions
In BASIC, operations within a numeric expression are performed following the order shown in Table
4-2. As in mathematical expressions, parentheses may be used to specify a part of an expression that
should be evaluated as an independent expression. See Table 4-5 for examples of arithmetic expressions
that demonstrate the evaluation order of operators with or without parentheses.

62
Expression After
Operation 1
After
Operation 2
After
Operation 3
After
Operation 4
Final
Result
3 * 2 + 5 6+5 11 11
3 + 2 * 5 3 + 10 13 13
(3 + 2) * 5 5 * 5 25 25
3 * 2 - 6 / 2 6 - 6/2 6 - 3 3 3
-2 * (3 - 1) ^ 2 -2 * 2^2 -2 * 4 -8 -8
((5 + 4) - 7) + 4 / 2 (9 - 7) + 4/2 2 + 4/2 2 + 2 4 4
Table 4‑5: Example Arithmetic Expression Evaluations
The rule for evaluating arithmetic expressions involving subexpressions in parentheses is first to evaluate
any subexpression within a pair of parentheses. The computation always proceeds from the innermost and
left-most pair of parentheses and works out until only a single value remains to represent the complete
expression that is contained in parentheses. In general, an expression may or may not contain one or
more subexpressions. Table 4-6 indicates how to proceed in evaluating an expression with parentheses.
We see how this rule is carried out in the expression:

63
Original expression: (3 + (2 - 4)) * (12 / 6) ^ 3
Evaluate (2 - 4) (3 - 2) * (12 / 6) ^ 3
Evaluate (3 - 2) 1 * (12 / 6) ^ 3
Evaluate (12 / 6) 1 * 2 ^ 3
Evaluate 2 ^ 3 1* 8
Evaluate 1*8 8
Table 4‑6: Evaluating Arithmetic Expression with Parentheses
4.4 Built In Functions
Functions that involve nontrivial computations are often part of a programming language that can be
viewed as “black boxes.” The programmer supplies the values needed by a function and BASIC returns
the required value using built-in code for the computation. Some of the useful functions in BASIC are
shown here:
SYNTAX
Built In Functions
BASIC FUNCTION NAME
Abs() Absolute value
Exp() Exponential function
Log() Natural logarithmic function
Sqr() Square root
On Your Own
1. Evaluate the following expressions.
(i) 2 + 8 - 6 * 3
(ii) (3 * 4) ^ 2 - (-5) + 9
(iii)4 ^ 3 * 3 ^ 2 * 8 / 4
(iv)10 / 5 * 8 - 9
(v) 5 * 3 * (8 - 3) / 4
2. Explain why the following statements are invalid and provide corrections for each.
x, y = 3 + z
x + y = z
3. List the order the operations are performed for each expression:
a) 3 - 2 / 4 * 6 ^ (2 - 3) + 5
b) (x1 * x2) / x3 ^ x4 - x5 + x6 ^ x7
c) x1 / (x2 + x3) * x4 / x5 ^ (x6 - x7)

64
A numerical expression may also contain any previously defined numeric variables. The following is a
valid assignment statement that contains a numeric expression.
overtime = (hours – 40) * 1.5 * wage
This statement computes an overtime payment based on the number of hours worked over 40. The
computer uses the hourly wage rate of one and one-half the hourly wage rate for each of the first forty
hours for the overtime wage rate. The result of the computation is assigned to overtime (puts the result
in the storage location assigned to the variable overtime).
Example 4‑1. Write a program that inputs a long jumper’s name and country along with three distances
jumped measured in meters. Using the three input distances, calculate the average distance jumped. Use
an output menu to display the input data and the calculated average.
OUTPUT:
Name: Samantha Jones
Country: USA
Jump 1 distance: 6.7
Jump 2 distance: 6.82
Jump 3 distance: 7
Average distance: 6.84

65
SOLUTION:
Rem Displays a long jumper’s distances for three
Rem jumps and the average of the distances
Rem INPUT: Personal info and three distances
Rem OUTPUT: Input values and average distance
Cls
Rem Get input
nam = InputBox(“Enter name:”)
country = InputBox(“Enter country:”)
jump1 = Val(InputBox(“Enter first distance:”))
jump2 = Val(InputBox(“Enter second distance:”))
jump3 = Val(InputBox(“Enter third distance:”))
Rem Calculate average
A ave = (jump1 + jump2 + jump3) / 3
Rem Display output
Rem Output personal info
Print “Name: “; nam
CurrentX = 30 * font_width ‘line is 9
Print “Country: “; country
Rem Output three jumps
Print “Jump 1 distance:”; jump1 ‘line is 11
Rem Output average
B Print “Average distance:”; ave

66
COMMENTS: In the solution program, line A is an assignment statement that contains a numeric
expression. The statement computes the average of the three given jumps. Notice that the program
includes B to display the value of the variable ave after it has been calculated.
On Your Own
1. Write a program that asks the user to enter a number of yards and a number of feet. The
program then calculates the number of inches that is equivalent to the given distance and
outputs that number.
2. Write a program that asks the user to enter the number of quarters, dimes, nickels, and
pennies that the user has. The program then calculates the total value of the coins as a
number of pennies and outputs that amount.
3. Write a program that converts miles per hour into kilometers per hour. A kilometer is .62 of
a mile.
4. Write a program that converts kilometers per hour into miles per hour. A kilometer is .62 of
a mile.
5. Write a program that converts hours, minutes, and seconds into seconds.
6. Write a program that converts years, months, and days into days. Assume 30 days in every
month.

67
4.5 Concatenation
Concatenation is a BASIC operation performed on two strings. Concatenation is the operation of
appending one string to the other. The ampersand () is the concatenation operator. For example, the
following lines of code concatenate strings:
s1 = “gotta”
s2 = “getaway”
s3 = s1 s2
Print s3
OUTPUT:
gottagetaway
Before the Print command, s3 has the value “gottagetaway” without a space. To insert a space between
the two words, you could include a space character as follows:
s3 = s1 “ ” s2
Concatenation can also be done with numeric values. To do this, BASIC first converts the numeric value
to a string and then performs the concatenation. For example:
price = 0.55
s = “One roll costs $”
t = s price
Print t
OUTPUT:
One roll costs $0.55
In this example price has a numeric value. When price is concatenated with s, BASIC converts the value
0.55 to the string “0.55” and uses the string in the concatenation.(“0.55” consists of four symbols: 0, .,
5, and 5.)
SYNTAX
Concatenation
Any combination of two literals or variables X1 and X2 joined by an
ampersand () generates a string with the character representation of
X1 followed by the character representation of X2.
EXAMPLE: “abc” “ def”= “abcdef”

68
4.6 Formatting Output
One of the problems programmers face when designing effective output schemes for a program involves
displaying computed results in an appropriate format. The code
x = 1 / 11
Print x
generates the output 9.090909E-02. This form is called exponential notation. The E-02 says to multiply
the number 9.090909 by 10-2
to get the normally expected value for this number. Computers usually
display numbers in exponential notation rather than having leading zero digits following the decimal
point. The notation is often referred to as a normalized representation of the value.
Although the exponential notation is well defined, the visual effect of such a number format is very
poor. BASIC provides the Format() function to control the format of displayed numbers and strings
of symbols. The idea is to prescribe the recipe for displaying digits or symbols of a value. We will only
discuss how Format() is used with numeric values. The value being printed may have quite a different
representation in memory. The Format() command does not change the memory representation of a
value but just describes how many of the digits or symbols in an internal representation will be displayed.
The example 1/11 will be more meaningful printed as 0.09 than as 9.090909E-02. When using the
Format() command, print positions on a line that will contain numeric values are described using zeros.
For example, if the value should be displayed with one digit to the left of the decimal point and two
decimal digits to the right of the decimal point, the format pattern would be represented by “0.00.” The
code that causes the formatting is supplied by the built-in-function Format(). The layout instructions
are written inside double quotes.
The formal syntax for this function involves two arguments, a value and a recipe. The SYNTAX box for
Format() gives the details.
SYNTAX
Format()
Format(variable or literal,“recipe”)
EXAMPLE: x = 1/11
Print Format(x, “0.00”)
RESULT: 0.09
The Format() function simply produces a string following the description given as the second argument
of the function. The Format() command can appear at any location in a list of values to be printed or
on the right side of an assignment statement. The code

69
mpg = 200 / 7
s = Format(mpg, “0.0”)
Print “Miles per gallon = “; s
produces this output:
Miles per gallon = 28.6
Notice that even though the format pattern only specified one digit to the left of the decimal point that
two digits are printed. The Format() function retains all of the digits to the left of the decimal point.
Digits to the right of the decimal point are rounded to match the specified precision. A dollar sign ($)
and a comma (,) can be included in the format pattern. The following code
total = 0.55 * 3030
s = Format(total, “$0,000.00”)
Print “Total cost is “; s
Total cost is $1,666.50
Notice that the trailing zero is printed. The zeros in the format pattern that follow the decimal point
specify the number of digits that will be printed.
BASIC has several useful built-in formats. Instead of specifying a pattern, you can use the string
“currency” as a format pattern. The following code
total = 0.55 * 3030
s = Format(total, “currency”)
produces the same output as the previous example. If the value has fewer digits to the left of the decimal
point than are specified by zeros in the format pattern then zeros will be produced. The following code:
total = 902.1
s = Format(total, “$0,000.00”)
Total cost is $0,902.10

70
BASIC has a different method of making columns of values while suppressing leading zeros. Use the @
sign instead of 0’s in the display description. If the number is not large enough to take up all the print
positions, leading blanks are printed. The following code shows how two numbers can be printed in six
print positions each, regardless of the size of the numbers.
Print Format(123,“@@@@@@”);Format(23456,“@@@@@@”)
OUTPUT: ___123_23456
In addition BASIC also has a built in recipe to display percentages. For example,
Print Format(.091, “percent”)
and the value will be displayed as 9.1%. To display a number with just two decimal digits use the word
standard in double quotes just as percent was used above.
Example 4‑2. Write a program that produces a table showing the sale prices of shovels ($3.78), axes
($4.98), and hammers ($5.65). The program should calculate and display the price of each item and the
price of each item after a 6% sales tax has been added.
OUTPUT:
Shovel Axe Hammer
Original $3.78 $4.98 $5.65
Taxed $4.01 $5.28 $5.99

71
SOLUTION:
Rem Produces a table that shows the original
Rem and taxed prices of three items.
Rem OUTPUT: Table of prices
Cls
shovel = 3.78: axe = 4.98 : hammer = 5.65
Rem Display the table header
Print ,
Print, “Shovel”, “ Axe”, “ Hammer”
Print “Original”,
Print , Format(shovel, “currency”),Format( axe, “currency”),Format( hammer, “currency”)
Rem Calculate the taxed prices
priceShovel = shovel * 1.06
priceAxe = axe * 1.06
priceHammer = hammer * 1.06
Rem Format the output
fPriceShovel = Format(priceShovel, “currency”)
fPriceAxe = Format(priceAxe, “currency”)
fPriceHammer = Format(priceHammer, “currency”)
Rem Display the taxed prices
Print “Taxed”,
Print ,fPriceShovel,fPriceAxe, fPriceHammer
COMMENTS: In the solution program, the header of the table is first displayed using the Print command.
The taxed prices are calculated based on the given original prices. Note the use of commas in the last
Print command to display the taxed prices below the original prices.
On Your Own
1. Form the following strings using concatenation where the numerical value is stored in the
variable nonString.
a) There are 18 students in the class.
b) WalMart operates 3165 stores.
c) The rugby team won by 35 points.
2. Write a program that asks the user for a bet on a horse in a horse race. For the prompt
concatenate a question with a numerical value of how much the user has. Store the
concatenation result in a variable and then use it in place of the prompt in InputBox().

72
Use CurrentX, CurrentY, and Format() statements to enhance the output for each of these programs.
1. Write a program that will prompt the user for five numbers and then display the sum and
average of those five numbers. Include appropriate commenting. Assume the numbers will
have between one and three digits after the decimal point.
2. Write a program to prompt the user for a temperature in Fahrenheit (for example, 30
degrees Fahrenheit). Convert that temperature to Celsius and display both values. Clearly
label the output and use comments to make your program readable. Use the equation
celsius = (fahrenheit – 32) * 5 / 9
to convert a Fahrenheit degree into an equivalent Celsius degree.
3. Write a program to prompt the user for a temperature in Celsius (for example, 30 degrees
Celsius). Convert that temperature to Fahrenheit and display both values. Clearly label the
output and use comments to make your program readable. Use the equation:
fahrenheit = 9/5 celsius + 3
to convert a Celsius temperature into its Fahrenheit equivalent.
4. Suppose the current currency conversion factor for converting US dollars into British
pounds is
1 Us = 0.6155 GBP.
For any amount of US dollars entered by the user, output the value of these dollars in terms
of the British pound.
5. The ABC Bakery charges $3.85 for a loaf of white bread, $4.65 for a loaf of whole wheat
bread, and $6.58 for a dozen dinner rolls. Write a program that inputs the number of loaves of
white bread (M), the number of loaves of whole wheat bread (N), and the number of dozens
of dinner rolls (Q) ordered. Compute the total cost of the order. Display the charge for each
item and for the cost of the total order. Use Format() for displaying the currency values.
6. Write a program that accepts as input the number of miles traveled and the number of
gallons of gas purchased. Output this data along with the number of miles per gallon for
this trip. Miles per gallon is the quotient of miles and gallons. Use an output menu for the
output.

73
7. Write a program that inputs two numbers and acts as a calculator. The program should
create an output menu that displays the sum, difference, product and quotient of the two
numbers. The output displayed should be similar to the following if 10 and 2 were the two
input numbers:
10 plus 2 is 12
10 minus 2 is 8
10 times 2 is 20
10 divided by 2 is 5
8. Write a program that prompts the user for the current amount due for a credit card. The
program then calculates the finance charge and determines the new balance. The finance
charge each month is 1.5% of the past due amount. The new balance is the sum of the past
due amount and the finance charge. For an input amount of 255.50, the output should be
similar to this:
Past Due Finance New
Amount Charge Balance
$0,255.50 $003.83 $0,259.23
9. Input the total number of miles a fleet of trucks drive in a week. If a truck get 7.86 mpg,
compute the number of gallons of gas the fleet uses in a week.
10.Write a program to compute the monthly payments for a loan. Run the program for the
three case given. The formula for computing the monthly payment for a loan of A dollars at
annualInt rate of interest for a length of months is:
Payment = A * (annualInt/12)/(1 + (annualInt/12))^(-months)
a) Joe Brown took a loan of $20,000 to buy a new car. If the payback period is 60
months and the interest rate is 1.9%, how much are the monthly payments?
b) The parents of Joe Smith took out a $35,000 loan to pay his tuition. If the interest
rate is 6.85% and the payback period is 120 months, how much will the monthly
payments be?
c) Jil Meyer graduated from college with $25,600 in student loan debt. If the annual
interest rate is 3.4% and the payback period is 10 years, how much are the monthly
payments?

74
11.Find the standard deviation of the following set of numbers: 8,12,9,11,7,5,4,3,13,11,9,18,16,1
The formula is:
var = 1/n*(x1^2 + … + xn^2) – ((x1 + … + xn)/n)^2
stDev=sqr(var)
where n is the number of numbers and x1, x2, … , xn are the actual numbers.
+ in + + ity
the of th + - c
- ste

75
Decision Making
5 Decision Making
In programming languages, decision making is a fundamental feature that involves comparisons between
two values and/or questions about the current state of a computation. As a result of asking questions about
values in a program, the program can either alter the flow of control or choose a proper computation
option for the value being processed. In this chapter, we introduce decision making in BASIC.
In a program to determine a letter grade for a set of scores the average of the grades is first computed. To
determine the letter grade the average is then compared with various ranges of numbers that correspond
to values representing the same letter grade. The results of the grade program are shown in Figure 5-1.

$YHUDJHJUDGHFRPSXWHG
/HWWHUJUDGHIRXQG
*UDGHVHDUQHG
Figure 5‑1: Computing a Letter Grade
5.1 Simple Comparisons
In programming languages, decisions are made based on comparisons. A comparison is evaluated
as either true or false. True and false are called logical or boolean values. Knowing the result of the
evaluation, a program can choose appropriate actions. In BASIC, comparisons can be made between
pairs of numeric values (numbers, numeric variables, and values of numeric expressions) or between
pairs of string values (character strings, string variables, and values of string expressions). Based on these
comparisons, the program chooses the code to be executed next.

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Decision Making
5.2 Numeric Comparisons
Numeric comparisons are those which involve the comparison of two numeric values. The relational
operators used in a numeric comparison are the same as those used in mathematics. In BASIC, numeric
comparisons are formed in a manner similar to comparisons in mathematics. We can compare pairs
of numeric values, variables or expressions. For instance, the following are valid numeric comparisons:
3 1
10 = 10
4 + 9 11
2 = 6 * 5
The BASIC relational operators and their numeric meanings are given in Table 5-1.
Operator Meaning
= equal to
not equal to
less than
greater than
= less than or equal to
= greater than or equal to
Table 5‑1: BASIC Relational Operators
You may already be familiar with the above relations when evaluating numeric comparisons involving
numeric values. However, you may be unfamiliar with evaluating comparisons that contain variable
names. The following are comparisons of numeric values represented by variables:
x = 10
y + 9 11
w = z * 5
w, x, y and z are variables with numeric values. In these comparisons, the computer first accesses the value
in the variable’s storage location. The accessed value is then used in the comparison. If a computation
involves an expression, the computation is carried out before the comparison is made. Comparisons are
always carried out with two values. A variable involved in a comparison must already have an assigned
value whether it is involved in a computation or not.

77
Decision Making
On Your Own
1. Explain why the following numerical comparisons are incorrect. Write correct versions of
these comparisons.
98
“dog” 47
2. Evaluate the following numeric comparisons as True or False. When evaluating variables
in these comparisons, assume the following assignments: A = 4, B = 9, C = 0.7, D = 22.
99 56
B A + 5
C = 0.07
1.002 = 1.02
A * B – C / D = 32
C * D C * A
give us a call on +44 (0)20 7000 7573.
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78
Decision Making
5.3 Strings
In BASIC, we can apply the relational operators to character strings as well as to numeric values.
Comparisons involving character strings are called string comparisons. However, before we can compare
strings, we must be familiar with the representation of character strings. With string comparisons it may
seem odd to say one string is less than another. When you understand that “smaller” means occurring
before in a dictionary of all possible strings, the idea is easier to grasp. A clear difference in BASIC is
that we do not have only 26 letters, but upper and lower case letters, numerals, and special symbols like
; that are all lined up in order just as we think of the English alphabet ordered from A to Z with A as
the first or smallest and Z as the last or largest.
5.4 Character Representation
A set of symbols is called an alphabet. A sequence of symbols from an alphabet written one after
another is called a word or a string. For now, let us use the capital letters of the English language (A, B,
C, …, Y, Z) as our alphabet. In general, we require an alphabet to have all the symbols ordered relative
to each other so that it is clear which symbol in the order occurs first when comparing two symbols.
In the English alphabet, we naturally order the letters from A to Z with upper and lower case letters
equivalent to each other. The computer represents each letter of this alphabet by a code value consisting
of a sequence of 0’s and 1’s that make up what is called a binary code. One code created to represent
symbols on a computer is called the ASCII-8 code. The ASCII-8 code for the capital letters of the English
language is given in Table 5-2.
Letter Binary Form Letter Binary Form
A 10100001 N 10101110
B 10100010 O 10101111
C 10100011 P 10110000
D 10100100 Q 10110001
E 10100101 R 10110010
F 10100110 S 10110011
G 10100111 T 10110100
H 10101000 U 10110101
I 10101001 V 10110110
J 10101010 W 10110111
K 10101011 X 10111000
L 10101100 Y 10111001
M 10101101 Z 10111010
Table 5‑2: ASCII-8 Code for A–Z

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Decision Making
When string variables or literals are used in a comparison, it is really the codes for the individual symbols
that are being compared.
5.5 Dictionary Ordering
Evaluating string comparisons is similar to looking up words in a dictionary. (The alphabet may be quite
different from the normal English alphabet.) The computer looks at the first letter in each of the words
and if they are different, evaluates the words according to which of these two letters occurs first in the
ordering of the alphabet (whatever set of characters is used). For instance, the following comparison is
true because “B” precedes “J” in the alphabet:
“BROWN” “JONSON”
It is not always possible to evaluate a condition by only looking at the first letter of a word. If two words
that begin the same but end differently are being compared, the computer performs the comparison at
the first letter position in the words at which different letters occur. This is just as in looking up words
in a dictionary. For example, in comparing the words “ANTS” and “ANTHRACITE” the first three letters
of both words are identical. If we were placing these words in alphabetical order (in a dictionary), we
would compare the “S” in “ANTS” to the “H” in “ANTHRACITE” to determine which word should occur
first in the dictionary. Since “S” occurs after “H” in the computer ordering of the upper case letters, we
conclude that the comparison
“ANTS” “ANTHRACITE”
is true. The computer begins at the leftmost character of each string and compares each corresponding
letter of each word until it finds a letter position in which the two letters of the two words are different.
In this case, the computer must compare the fourth letter of each of the words to conclude that this
comparison is true. Notice that the length of the words compared did not determine the order. Another
way to evaluate a string comparison is to first translate the symbols to their ASCII-8 codes and then
compare the numbers these codes represent. For example, let us examine the comparison from above:
“BROWN” “JONSON”
Since the first letters of each of these words are different, we need only to compare the first letters. If
we look up the ASCII-8 code for the first letter in each string, we find the binary number 10100010
represents “B” and similarly the binary number 10101010 represents “J.” We can look at the ASCII-8
code for each letter as a string from the alphabet {0, 1} and look for the first position in which these
words have a different letter of this alphabet. For just the codes for B and J we see

80
Decision Making
%
-
where the fifth position has a 1 in “J” and a 0 in “B.” We conclude
“J” “B”
If we wish to compare two words which begin the same but end differently as in the comparison,
“ANTS” “ANTHRACITE”
we can simply compare the ASCII-8 value of “S” to the ASCII-8 value of “H”. We find that
6 ! +
is true, and thus, the original comparison, “ANTS” “ANTHRACITE,” is true as well.
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81
Decision Making
For words of different lengths, we pretend that the shorter word has blanks attached onto the end of
the word so that each of the words is viewed as having the same length. The ASCII-8 code assigned
to a blank is always less than the code of any letter of the alphabet. So if we are comparing two words
that begin identically and only differ when one of the words runs out of letters to compare, the shorter
word will be less than the longer word. Again, this is as in a dictionary. For example, the comparison,
“CAT” “CATS”
is true because the “fourth” letter of the two words are a space and an “S.” (The ASCII-8 code for a space
is less than the code for “S.”)
C A T Space
C A T S
Figure 5‑2: “CAT” “CATS”
Computers use a code for the symbols to correspond to our expectations about the order of the letters
of the English alphabet, one code, the ASCII-8 code, arranges binary representations so that
space ”A” “B” “C” ··· “Z”
This alphabetic ordering allows us to compare character strings just as we would look up two words in
a dictionary. However, we may encounter certain symbols that are not listed in the alphabet of English
letters. For example, we may choose to compare symbols such as (, }, ?, or !. We may also compare
character strings that contain digits. The digits all follow the letters of the alphabet in the ASCII-8 code.
Also, the ASCII-8 code is assigned so that
“0” “1” “2” ··· “9”
Thus, the following comparison is true:
“318A” “215B”
In addition, BASIC distinguishes between uppercase and lowercase letters in a character string. Uppercase
letters and lowercase letters have different ASCII-8 codes. Lowercase letters follow the uppercase letters
in the ASCII-8 code. So, for example, the following comparisons are true:
“yes” “YES”
“Yes” “YES”

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Decision Making
Keep in mind that variables involved in comparisons must already have assigned values. Also, note that
programs should not compare numeric values to character strings and vice versa. For more examples
of BASIC comparisons and their results, see Table 5-3.
Comparisons Results
5 3.9 True
-3 -2 True
“cat”= “cats”space “s” False
“5B”= “and”“5” “a” False
“hello”= “HELLO”“h” “H” False
“conf-90” “conf-91”“0””1” True
“Jane” “jane”“J” “j” True
Table 5‑3: Comparisons and Results
On Your Own
1. Evaluate the following string comparisons as true or false. When evaluating variable
comparisons, assume the following assignments: name1 = “Smith”, name2 = “Jones”, name3
= “Smithe”.
“dog” “dogs”
name2 = name1
“house” = “HOUSE”
“(example)” “example”
“6G” = “7G”
name1 name3
6.6 String Comparisons
Now that we know how characters are represented and how their codes are ordered so that we can
compare strings, we need to list all the relational operators and their meanings for string comparisons.
See Table 5-4.
Operator Meaning
= identical to
different from
precedes alphabetically
follows alphabetically
= precedes alphabetically or is identical to
= follows alphabetically or is identical to
Table 5‑4: Relational Operators in String Comparisons

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Decision Making
Just as with numeric comparisons, string comparisons can be performed on either character strings or on
variables representing character strings. For instance, the following are valid BASIC string comparisons
assuming the character variables name1, phone1, and phone2 have been assigned values.
“cat” “ball”
“sale-89” = “sale-90”
name1 = “Jane”
phone1 phone2
6.7 Conditional Statements
A fundamental feature of BASIC is the syntax that allows conditions to be evaluated by a program as a
means of controlling the order of execution of statements in a program. Often decision making is done
based on a statement that involves a comparison. Comparisons are evaluated to be either true or false. The
idea is to be able to carry out certain actions when a condition evaluates to be true. This kind of statement
is called a conditional statement. In BASIC, conditional statements are implemented using an If block.
5.8 Simple If Blocks
The syntax of a simple If .. Then .. End If block is:

84
Decision Making
SYNTAX
Simple Condition
If .. Then .. End If
If condition Then
Action when condition is true
End If
EXAMPLE: If surName = “M” Then
surNameEdited=surname “, “
Print surNameEdited; firstName
End If
A block of code as shown in the SYNTAX box contains markers, which are necessary keywords that
indicate the beginning and end of certain parts of a block of code. An If-block always contains at least
three markers. These three markers are If, Then, and End If. Following the If marker is a condition that
is evaluated. The condition is a comparison, either numeric or string. Following the condition is the
Then marker that indicates the end of the condition and the beginning of the true range.
The true range consists of statements that are executed when the condition is true. We sometimes refer
to Then as a guard for the true range that only lets the execution into the true range when the condition
is evaluated to be true. Ending the true range is the End If marker.
When an If block is executed, the condition is first evaluated. If the condition is true, the actions specified
in the true range are performed. The program then continues execution at the statement following the End
If marker. If the condition is false, the program will continue execution of the program at the statement
following the End If marker. See Figure 5-3 for an example of a simple If block.
a = Val(InputBox(“Enter a number”))
If a 0 Then
sq = a * a
Print a; “ squared is “; sq
End If
Figure 5‑3: Example of a Simple If block
In Figure 5-3, notice the spacing conventions used within an If block. The statements following the Then
marker are indented. This convention clarifies which actions should be performed if the condition is
true and also where the statement(s) in the true range of the If-block ends. One key to understanding
programs involves identifying the different parts of the code. This identification process is made easier by
a consistent indentation style for different kinds of statements. Regardless of the indentation conventions
followed, every true range of a simple If ends with the marker End If.

85
Decision Making
On Your Own
1. Write a program that inputs the outside temperature. Use an If-block to check if the
temperature is greater than 70. If it is, print a message saying “Wear shorts today.”
2. Write a program that inputs the weight of a salmon caught. Use an If-block to check if
the weight is greater than 10 pounds. If the salmon weighs more than 10 pounds, print a
message saying “Great fish!”
5.9 The Else Option
Sometimes in an If block, you may want to specify one set of actions to be performed if the condition is
true and a different set of actions if the condition is false. In this case, we use the Else marker as shown
in the following SYNTAX box:

86
Decision Making
SYNTAX
Two Way Condition
If .. Then .. Else .. End If
If condition Then
Action when condition true
Else
Action when condition false
End If
EXAMPLE: If surName = “N”Then
surNameEdited=surname “, “
Print surNameEdited; firstName
Else
Print “Name out of required range”
End If
The condition in the example is true if the value of surName starts with any letter greater than “M” (after
M in the English alphabet). The Else marker appears after the true range and marks the beginning of
the false range, which consists of the statements to be executed if the condition is evaluated to be false.
Ending the entire If-block as well as the false range is the End If marker.
If the condition is true, program control is passed to the first statement in the true range. The statements
in the true range are then executed. When those statements have been completed, the program encounters
thekeywordElse,theprogramthencontinuesexecutionatthestatementfollowingEndIf.Ifthecondition
is evaluated to be false, program control is passed to the first statement in the false range which is the
first statement after the keyword Else. When those statements following Else and preceding End If have
been executed, program control is passed to the first statement following End If.
Figure 5-4 contains an example of an If .. Then .. Else .. End If block. Notice the indentation for this
block. It is helpful to follow these spacing conventions in programs you write.
answer = InputBox(“Enter a word:”)
If answer = “anthracite”Then
prize = 100
Print “Word matches! You win: “, prize
Else
prize = -100
Print “No match. You lose: “,prize
End If
Figure 5‑4: Example of an If Block with an Else Option

87
Decision Making
As you can see from the code, the program is checking to see if an answer given matches the program’s
answer. If the answer is correct (the condition is true), you win $100. If the answer is incorrect (the
condition in false), you lose $100. Observe that there are no $-signs in the code. A $-sign appears only
in output when using a Format statement or including a $-sign in a string constant.
Example 5‑1. Use an If…Then…Else…EndIf block to write a program that inputs two different numbers
and prints the two numbers in decreasing order.
© Deloitte Touche LLP and affiliated entities.
360°
thinking.
Dis
Deloitte Touche LLP and affiliated entities.
360°
thinking.
360°
thinking.

88
Decision Making
SOLUTION:
Rem Determine which of two unequal
Rem numbers is the larger.
Rem INPUT: Two numbers
Rem OUTPUT: The numbers entered in decreasing order
Cls
Rem Get input
num1 = Val(InputBox(“First number:”))
num2 = Val(InputBox(“Second number:”))
Rem Decide which is large
If num1 num2 Then
Print num1; “ is greater than “; num2
Else
Print num2; “ is greater than “; num1
End If
On Your Own
1. Write a program that inputs a person’s age. Print the age. Also print the message “Vote Nov.
5!” if the age is greater than 18. Otherwise, print “You’re too young to vote.”
2. Write a program that inputs a number indicating which meeting group you are in. If your
number is less than 3, print “You get special seating.” If the group number is 3 or greater,
print “You are on standby.”
5.10 Compound Conditional If Blocks
Simple conditions do not always reflect what is needed to be known in a program. In such cases, an If
block based on a combination of conditions being true or false is needed. For example, if you want to
know if a person is male and older than 18, you will need two conditions to be satisfied at the same time.
The logical operators used to combine simple comparisons are And, Or and Not.
You have seen how to determine whether a numeric or string condition is true. To determine whether
a compound condition involving two conditions is true or false, the computer must determine the truth
value for each of the simple conditions separately and then combine those truth values as indicated in
Table 5-5 using the logical operator And.

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Decision Making
And Condition Truth Value For
Condition 1
Truth Value For Condition 2 Truth Value For Condition 1 And
Condition 2
POSSIBLE False False False
TRUTH False True False
VALUE True False False
True True True
Table 5‑5: Truth Table for the And Operator
Table 5-5 is called a truth table for And since it represents in tabular form how the truth values of the
individual conditions are combined to find the truth value of the compound condition.
Figure 5-5 shows an If block with two conditions joined by the And operator. On each side of And there
must be a correctly written condition.
color3=”orange”
color1=InputBox(“Enter a color”)
color2=InputBox(“Enter a color”)
If (color1 = “red”) And (color2 = “blue”) Then
color3 = “purple”
End If
Figure 5‑5: Code with If Block and the And Operator
In the example in Figure 5-5, both of the conditions must be true in order for the assignment of
“purple” to color3 to be executed. Also, notice in Figure 5-5 that if more than one condition is tested,
each condition is surrounded by parentheses. Surrounding the simple conditions with parentheses can
make them easier to read.
WARNING: As another example, suppose we want to test whether a variable has a value greater than 0
and less than 200. The condition could be written as:
0 years 200
as one does in algebra. Although this is perfectly correct in mathematical contexts, BASIC does not allow
this syntax as a substitute for what was shown in Figure 5-5 for testing the two colors. This condition
must be written as
(0 years) And (years 200)
Along the same lines, we can also use the operator Or between conditions. When Or is used to join
two simple conditions, at least one of the individual conditions must be true in order for the compound
condition to be true. See Table 5-6 for the truth table of the Or operator.

90
Decision Making
Or Condition Truth Value For
Condition 1
Truth Value For
Condition 2
Truth Value For Condition 1 Or
Condition 2
POSSIBLE False False False
TRUTH False True True
VALUES True False True
True True True
Table 5‑6: Truth Table for the Or Operator
The Not operator negates the value of a comparison: if the comparison is true then the Not operator
changes the result to false and vice versa. The truth table for Not is shown in Table 5-7.
Not Condition Truth Value For
Condition
Truth Value For Not
Condition
TRUTH False True
VALUES True False
Table 5‑7: Truth Table for the Not Operator
An example of using the Not operator is shown here:
Condition 1: miles 5000
Condition 2: Not (miles 5000) is the same as miles = 5000
The condition
Not ((A 3) And (B 4))

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Decision Making
is logically equivalent to
Not (A 3) Or Not(B 4)
which is logically equivalent to
(A = 3) Or (B = 4).
This condition is not the same as
Not (A 3) And Not (B 4)
as you can readily see if you let A = 2 and B = 3.
When you want to verify a variable, say criterion, has one of a small set of possible values, such as criterion
must be 1 or 2 or 3, you can check this by first asking if criterion has one of the values as:
(criterion = 1) Or (criterion = 2) Or (criterion = 3)
If you are only concerned that criterion has some legal value and action is only required if criterion does
not have a required value, use the previous condition along with Not as:
Not ( (criterion = 1) Or (criterion = 2) Or (criterion = 3) )

92
Decision Making
The compound condition inside the outer most pair of parentheses is true if criterion has a required
value. The Not operator makes the condition false in that case. If criterion does not have one of the
required values, the compound condition inside the parentheses evaluates to false since each of the
simple conditions is false and the Not operator outside makes the whole condition true.
On Your Own
1. Explain why the following compound conditions are incorrect.
a) temp 60 And 75
b) rating = “G” Or “PG”
c) answer1 And answer2 = 63
d) 12 = num1 = 17
Example a) is particular enticing when you want to test whether a variable has one of a set of
values. In BASIC this can be done only as
temp 6 And temp 75
2. For a variable XYZ with a numerical value, write conditions to test if the value of XYZ is:
(a) greater than 30; (b) less than 80; (c) greater than or equal to 91; (d) less than or equal
14; (e) greater than 50 and less than or equal to 90; (f) greater than 60 or less than 20; (g)
greater than 70 and greater than or equal to 25; (h) not less than 40 (use Not); (i) is one of
the values 1, 2, 3, or 4; (j) is not one of the values 3, 5, 7, or 11 (use Not).
3. For a variable ABC with a string as its value, write conditions to test if the value of ABC is:
(a) greater than “abc”; (b) less than “race”; (c) greater than or equal to “class”; (d) less than
or equal to “Smith”; (e) greater than “base” and less than or equal to “call”; (f) greater than
“expert” or less than “alfa”; (g) greater than “same” and greater than or equal to “equal”; (h)
not less than “major” (use Not); (i) is one of the strings “ab”, “cd”, “sf”, or “g”; (j) is not one of
the strings “sue”, “jane”, “bill” or “sam” (use Not).
4. For variables W, X, Y, Z each containing a numerical value, write conditions to test whether
the following questions about the values are true or false: (a) the value of W is greater than
either the value of Y or the value of Z; (b) The value of Z is less than or equal to any of the
values of the other variables; (c) the value of Z is greater than either the value of W or the
value of X while the value of Y is not less than the values of either X or Z; (d) the values of
W and X are each greater than the value of Z while the value of Z is strictly less than the
value of Y and the value of Z is not equal to the value of X. Would there be any difference in
the conditions if the variables contained strings instead of numeric values?

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Decision Making
5.11 Multi-case If Blocks
A university often needs to process student records for current students according to the year of
expected graduation. Typically, this problem becomes at least four different problems depending on
the graduation year. If the information about a student contains a variable named code whose value
indicates the graduation year of the student, the following commands use the coded value to determine
a graduation year:
If code = 4 Then
YEAR = 2014
End If
If code = 3 Then
YEAR = 2015
End If
If code = 2 Then
YEAR = 2016
End If
If code = 1 Then
YEAR = 2017
End If
We have simply written four separate If blocks, one for each case. Each value of code yields a value of
true for exactly one of the four conditions. However, this code is inefficient since the computer will
check each condition, even if the first condition is true. For example, if code = 4 is true, we assign 2014
to YEAR and then ask if the code has value 1, 2, or 3. Thus, for efficiency, we can subdivide an If block
to include more than two cases by using the syntax associated with the ElseIf marker. We see this
construction in the next example.
Example 5‑2. Write a program that inputs a student’s name and class code. Associate the input class
code with a graduation year and display the year of graduation. Use an If block with the ElseIf marker
to produce a case statement.
SAMPLE OUTPUT:
Bart Simpson
Class of 2015

94
Decision Making
SOLUTION:
Rem Inputs a student’s name and
Rem class code and output the student’s name
Rem and graduation year.
Rem INPUT: Name and class code
Rem OUTPUT: Name and graduation year
Cls
Rem Get input
nam = InputBox(“Student’s name.”)
code = Val(InputBox(“Class code (1, 2, 3 or 4).”))
Rem Determine year
A If code = 4 Then
yr = 2014
B ElseIf code = 3 Then
yr = 2015
C ElseIf code =2 Then
yr = 2016
D Else
yr = 2017 ‘assume code has a valid value
E End If
Rem Display output
F CurrentY = 8 * font_height
Print nam
Print “Class of”; yr
COMMENTS: In the solution program, the user is asked to enter a class code with value 1, 2, 3 or 4. This
input is assigned to the variable code. The If block beginning in A and ending at E then acts as a case statement
and associates each code with a graduation year: 2014 if code = 4; 2015 if code = 3; 2016 if code = 2; and
2017 if code = 1.The marker pairs in the If block are If .. Then (A), Then .. ElseIf (A-B), ElseIf .. Then (B),
Then .. ElseIf (B-C), ElseIf .. Then (C), Then .. Else (C-D), and Else .. End If (D-E). Starting with A, the
value of code is compared to 4. If code = 4 is true, then yr is assigned the value 2014 and control passes to F.
If code = 4 is false, then the condition code = 3 is tested. If code = 3 is true, then yr is assigned the value 2015
and control passes to F. If code = 3 is false, then the condition code = 2 is tested. If the condition code = 2 is
true, then yr is assigned the value 2016 and control passes to F. If code = 2 is false, the code between the two
markers Else and End If is executed. In this case yr is assigned the value 2017 and control then passes to F.

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Decision Making
ThesyntaxofBASICrequirescompleteconditionsbetweenIf..ThenandbetweeneachElseIf..Then.There
is no condition following Else and this is interpreted to be any case not singled out by the explicit conditions
tested. For example if code could be one of the values 1, 2, 3, 4, 5, or 6, then for all the occurrences of the
values 1, 5, and 6, the variable yr would be assigned the value 2017. If code would have an incorrect value,
you could test directly for 1 and use the else code to indicate an error. Using the ElseIf marker to write this
block is more efficient than writing four separate If blocks, one for each of the four situations. Rather than
testing four different conditions, the variable yr receives a value as soon as the code is identified, and then
program control drops out of the If block. The ElseIf marker must be written as a single word, not as Else If.
We have seen several forms of the standard If block: the If block with the And operator, the If block
with the Or operator, and the If block with more than two cases. The If block gives a powerful tool for
program design.
SYNTAX
Multi-Case Ifs
If .. Then .. ElseIf .. Else .. End If
If condition1 Then
Action1
ElseIf condition2 Then
Action2
ElseIf
.
.
.
Else
Action
End If
EXAMPLE:
If num = 90 Then
Print “A”
ElseIf num =80 Then
Print “B”
Else
Print “C”
End If

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Decision Making
On Your Own
1. Explain why the following If blocks are invalid.
(a) If total = 90 Then
Print total
(b) If i 15
Print “Fifteen”
End If
(c) If mat = 3 Then
sum = 12
Else If mat = 4 Then
sum = 15
Else mat = 6 Then
sum = 18
End If
2. Identify the output of the code:
If x .9 Then
die = 1
ElseIf x .8 Then
die = 2
ElseIf x .7 Then
die = 3
Else
die = 6
End If
For input values x = .67, .81, .45, and .94.

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Decision Making
Example 5‑3. A local internet cafe charges $0.50 for the first 30 minutes online and $0.15 for each
additional 10 minutes or fraction of an additional 10 minutes. Using an If block, write a program that
inputs the number of minutes of the session and outputs the cost and length of the session.
SAMPLE OUTPUT:
The cost is $1.80 for using the internet for 47 minutes.
SOLUTION:
Rem Calculate the cost for internet connect session. The rate is $0.50
Rem for the first 30 minutes and $0.15 for each additional ten minutes
Rem or part of an additional 10 minutes.
Rem INPUT: Number of minutes logged on.
Rem OUTPUT: The cost and the number of minutes charged
Cls
Rem Get input
minutes = Val(InputBox(“Minutes of internet use:”))
Rem Calculate cost
A If minutes = 0 Then
cost = 0
B ElseIf minutes = 30 Then
cost = 0.5
Else
C over = (minutes – 30) / 10
If over Int(over) Then
over = Int(over) + 1
End If
D cost = 0.5 + over * 0.15
End If
Rem Display output
Print “The cost is “; Format(cost, “currency”);
Print “ for using the internet for”; minutes; “minutes.”
COMMENTS: The condition in line A determines whether or not we logged in correctly. If the length
of time was zero minutes, there is no charge. The condition in line B ensures that if the session was
completed within 30 minutes, the cost of the session is $0.50. Otherwise, an additional charge is calculated
for each 10 minutes or fraction of 10 minutes over the original 30 minutes (lines C and D). The ElseIf
syntax does the same thing as

98
Decision Making
If minutes = 0 Then
cost = 0
End If
If (minutes 0) And (minutes = 30) Then
cost = 0.5
End If
If minutes 30 Then
over = over / 10
If over Int(over) Then
over = Int(over) + 1
End If
cost = 0.5 + 0.15 * over
End If
On Your Own
1. Write a program to handle a savings account withdrawal. Request from the user the current
balance and the amount of the withdrawal. If the withdrawal is greater than the original
balance, the program should display “Withdrawal denied.” If the withdrawal is allowed, the
program should then display the new balance. If the new balance is less than $50.00, the
program should also display “Balance below $50.00”.
1. Write a program that takes as input a sales person’s name and number of sales for the day. If
the number of sales is over 300, print the following message:
Good job! You will get a bonus!
Otherwise, print the following message:
Too bad! Try harder next time!
2. Ajax drivers get $0.75 per mile for each of the first 300 miles they drive. They are
reimbursed at the rate of $1.19 per mile for all miles over 300. Write a program to compute
a driver’s payment if the total number of miles driven is input.
3. Ajax keeps a log of the number of miles each truck has been driven. Every two months (8
weeks) the company totals up the miles for each truck to determine what maintenance is
needed. Suppose that a truck that has been driven more than 350 miles is scheduled for an
oil change, a lube, and a washing. If a truck has been driven up to 350 miles, just a wash is
scheduled. Write a program to compute the total miles a truck was used and output both the
total miles and the kind of maintenance to be scheduled for that truck.

99
Decision Making
4. Write a program to enter a student’s name and percentage grade on an exam. The program
should then display the student’s name, percentage grade, and a corresponding letter grade.
Use the following table as a guide to the cutoff points for the corresponding letter grades:
Cutoff Point Letter Grade
90 A
80 B
70 C
60 D
below 60 F
5. Write a program that calculates the cost of sodas for a picnic. Sodas cost 21 cents each when
fewer than 100 sodas are purchased. The cost is 19 cents per soda when 100 or more sodas
are purchased. The user should input the number of sodas purchased. Modify the program
so that the company ordering the sodas is identified.
6. Write a program that calculates the gross pay of an hourly employee if the hourly wage is
$10.75 for the first 40 hours and 1.5 times that for all hours over 40. The user inputs the
number of hours worked.
7. Write a program that inputs integers a and b. Determine if a divides b, i.e. there is no
remainder. (Use the Mod operator: the value of b Mod a is the remainder of dividing b by a.
For example, 6 Mod 4 = 2.)
8. Write a program that requests the lengths of three line segments as input and tells whether
the lines can form a triangle. Three lines can form a triangle if the length of the longest line
is less than the sum of the lengths of the other two lines.
9. Input the number of widgets a customer buys. Widgets cost $7.16 for the first eight and
$6.78 for any others, compute the total cost of a customer’s purchase.
10.Input the number of widgets a customer buys. The cost is $7.95 each for the first five, $7.65
each for the next five, and $7.02 for all additional widgets. Compute the cost for sales of 4, 6,
9, 11, and 21 widgets.
11.Using a grading scale of:
A 90-
B+
88–89
B 80–87
C+
78–79
D 0–69
Compute a grade for a score entered by the user.

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Decision Making
12.For any number in the range 0–500 determine the quality of the value according to the
following table:
0–125 Marginal
126–385 Acceptable
386–415 Well above average
416–500 Exceptional.
For output display the range for the category of the value entered and its value.
13.Suppose the mean (m) of a set of number is 86 and the standard deviation (stDev) is 16. For
any value input determine its grade using the following table:
Less Than Greater Than Or Equal Grade
m – 2 * stDev Not Passing
m – .75 * stDev m – 2 * stdev C
m + stDev m – .75 * stDev B
m + stDev A
14.An aptitude test has two parts. The score in each part range from 0–50. Enter a person’s
scores on each part and determine the evaluation given by the following table where the
Part I score is given if the Part II score is above the range for that Part I score.
Part I Part II Evaluation
0–20 0–10 Retake in 30 days
21–35 11–25 Take practical test
36–50 26–50 Certification completed

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Branching
6 Branching
Often in problem solving, the execution of an algorithm comes to a point at which the next steps of the
processing depend on the current value of some variable. In fact, different values may require different
kinds of processing or different blocks of code. This ability to switch execution to different blocks
of code depending on the current state of the program is called branching. Branching exists in two
forms: conditional and unconditional. In unconditional branching whenever a branching command
is encountered, the program automatically switches control to the block of code indicated. On the other
hand, when using an If block, we can implement conditional branching. In this case the program
branches to the block of code indicated only when the condition located between If and Then is true.
A typical application of branching involves some type of processing a set of data values. Finding the
average of a set of numbers uses this strategy. Obviously, the average cannot be computed until all the
values have been summed and counted. The program if Figure 6-1 has one block of code that accumulates
the values and counts how many there are. A second block of code is switched to when the summing is
finished so that the average can be computed

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Figure 6‑1: Summing and then Computing an Average
6.1 Line Labels
When branching is done in a program, there must be some way to indicate the program statement to
which the program will branch. To identify a statement that is the object of a branching command, we
use line labels. A line label in a program merely serves as a marker telling BASIC to remember the
location of this statement in the program.

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Branching
For clarity and uniformity, we use a restricted form for line labels. Except as a parameter for a transfer
statement, a line label may only appear before the first executable instruction in a line of a program.
Secondly, though line labels may be formed using the same rules as for forming variable names, the
labels we use always begin with the capital letter L followed by an integer value of one or two digits.
Finally, a BASIC requirement is that the label must be followed by a colon (:). The colon is used to
separate statements on a single line or to separate a line label from a statement. For example
L1 : X = 2
is valid because the line label and the assignment statements are separated by the syntactic unit (:) that
is used only for that purpose. If a line label is being used as an argument in a branching command, no
colon is needed. The following are examples of line labels:
L1
L13
L77
SYNTAX
Line Label
Variable separated from a statement by a colon. The
value of the line label is the address of the storage
location for that line of code.
6.2 Unconditional Branching
In BASIC, unconditional branching results by using the GoTo command. This command allows
branching from any statement in a BASIC program to any other statement identified with an appropriate
line label. The GoTo command takes one line label as an argument. When a GoTo command is
encountered, the control of the program is automatically and immediately transferred to the line specified
by the line label. The following are valid GoTo statements:
GoTo L1
GoTo L13
GoTo L77
In a GoTo statement there is no colon following the line label because the line label is not being used
to mark a line of code. In this case the value of the line label is the location of the next statement in the
program to be executed.

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SYNTAX
GoTo command
A command that transfers control to the location
that is the value of the variable.
On Your Own
1. Explain why the following GoTo statements are invalid.
GoTo
GoTo L1, L3
The program in Figure 6-2 demonstrates unconditional branching with a GoTo statement and a line
label. Pay close attention to the conventions used in line labeling.
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Rem Program to demonstrate the
Rem GoTo command.
Cls
Print “Hello World!”
Print “How are you?”
A GoTo L1
B Print “I’m fine.”
C L1: Print “Goodbye!”
Figure 6‑2: Unconditional Branching with GoTo
The output of the program is the following:
Hello World!
How are you?
Goodbye!
Notice in the execution of the program that line B was not executed. When the program executed the
GoTo command in A, the control of the program jumped to the line labeled L1 (C) where the program
continued execution. This branching caused statement B to be skipped. One of the problems with using
GoTo statements without being very careful is that you could cause an important statement to be skipped.
This example program may seem trivial, but it does illustrate the semantics of the GoTo statement rather
vividly. The GoTo command will be quite useful later as we discuss conditional branching and looping.
On Your Own
1. Using a GoTo statement and a line label, edit the following program to display only the
message “Good Evening.” The program should not display the message “Good Morning.” Do
not remove any lines from the program. You need only to add one GoTo statement and one
line label in the correct positions.
Rem Program prints two lines of text
Rem but will be edited to print only one.
Cls
Print “Good Morning.”
Print “Good Evening.”

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Branching
2. Using a GoTo statement and two line labels, edit the following program to display only
the message “Good Morning.” The program should not display either the message “Good
Evening” or the message “Good Day.” Do not remove any lines from the program. You need
only to add two GoTo statement and two line labels in the correct positions.
Rem Program prints two lines of text
Rem but will be edited to print only one.
Cls
Print “Good Evening.”
Print “Good Morning.”
Print “Good Day.”
6.3 Repetition of Code
A fundamental problem that will be explored in this and especially the next chapter involves processing
multiple pieces of data in the same way. For example, suppose a program needs to add up three data
values. The program could be the one shown in Figure 6.3.
Rem INPUT:Three values
REM OUTPUT: Sum of the values entered
REM Initialize accumulator
sum = 0
REM Process the first data value
A x = Val(InputBox(“Enter value”))
B sum=sum + x
REM Process the second data value
C x = Val(InputBox(“Enter value”))
D sum=sum + x
REM Process the third data value
E x = Val(InputBox(“Enter value”))
F sum=sum + x
REM Output sum
Print sum
Figure 6‑3: Summing Three Values
The first observation is that it is fortunate the program does not have to sum up 100 values! The second
observation is that the two lines A and B are identical to the two lines C and D and the two lines E and F.

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Branching
What would be convenient is to reuse lines A and B three times instead of writing the same code three
times. Programming languages incorporate a way to do just this. We can use the same code over and
over by incorporating conditional branching into the code.
6.4 Conditional Branching
In computer programming, conditional branching implies that program control is transferred from
one statement to another only when a certain condition is true. In BASIC, conditional branching can be
achieved by using the GoTo command within an If block. For instance, the code in Figure 6-4 produces
conditional branching-branching only if the variable switch has the value 1 when the program executes
this statement.
If switch = 1 Then
GoTo L1
End If
Figure 6‑4: Conditional branching
In the code of Figure 6-4, the condition switch = 1 is the test. If the condition is true, the GoTo command
in the true range causes control to transfer to the line labeled L1. If the condition is false, the program
continues execution at the statement following the End If.
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Branching
To this point the programs shown have simply executed lines of code one after another in order from
the start to the finish of the program. Usually a more complex program needs to repeat some of its lines
of code several times in order to solve a problem. For example, in the next program, we want to add
up a sequence of numbers that are entered by the user until the sum of the numbers entered exceeds
100. The program will repeat part of the code until the sum of the input values exceeds 100. This will
be accomplished using conditional branching
Example 6‑1. Using conditional branching, write a program that inputs and adds numbers until the total
of the numbers input exceeds 100. The program should print the numbers entered and the final total.
SAMPLE OUTPUT:
Number entered: 5
Number entered: 9
Number entered: 11
Number entered: 46
Number entered: 60
The sum of the numbers is 131
SOLUTION:
Rem Program inputs, displays, and adds numbers until the total
Rem of the input values exceeds 100. The final total is then displayed.
Rem INPUT: Numbers to add
Rem OUTPUT: Input numbers and final total
Cls
Rem Initialize the total
A total = 0
Rem Enter a numeric value
L1: num = Val(InputBox(“Enter a number:”))
Rem Process the value entered
Print “Number entered:”; num
B total = total + num
Rem Check the total
C If total = 100 Then
D GoTo L1
End If
Rem Display output
E Print “The sum of the numbers is”; total

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COMMENTS: In the program the variable total is set to zero (A) so that it can be used as an accumulator
for the sum of the input values. The variable total starts at zero because it should be equal to the sum of
the values processed when the program executes (A). We then ask the user to input a number and add
that number to total (B). The value of total is then compared to 100 (C). If the value is less than or equal
to 100, the condition is true, and the GoTo statement (D)- the true range of the condition-transfers the
program control to the statement labeled L1. Execution continues with the statement at that line. The
next number is then entered and processed. The input and processing code is repeated until the condition
in C is false. When the condition (C) is false, the program continues at E and displays the output. This
program is a typical example of the use of conditional branching in a BASIC program.
Though the GoTo command can be helpful in several situations, we do not recommend using it often.
Frequent use of the command may create complicated programs that are difficult to understand, debug
and change. Thus, use the GoTo command sparingly and carefully.
SYNTAX
Unconditional and Conditional Branching
Unconditional branching: Simply a GoTo statement that is
executed whenever it is encountered
Conditional branching: A GoTo statement that is in the
true range of an If statement so that it may or may not be
executed
On Your Own
1. Using one or more GoTo statements, write a program that displays on the screen the list of
even numbers from 2 to 20 as well as the sum of these numbers. Also print the partial sum
at each stage of the computation. After displaying 20, the program should print the message
“Task complete.”
Hint: Use a variable called num and initialize it to 2. Also initialize a variable total to zero to
use to accumulate the sum of these numbers. Also, somewhere in your program include the
following line of code:
num = num + 2
so that the program can test the current value of num to determine whether the termination
condition is satisfied.

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6.5 Repetition a Number of Times
In addition to using conditional branching with the condition asking about the value of some variable
in the program, conditional branching is often used when the condition involves how many data values
have been processed. By knowing ahead of time how many data items are going to be processed, the
condition can just use a counter that knows how many data values have been processed to know when
all the data has been processed. An example of this technique is shown in Example 6-2.
Example 6‑2. Input the 10 scores for the May baseball games of the Lions. Determine how many games
the Lions won in May.
SOLUTION:
Rem Program inputs 10 baseball game scores and determines
Rem how many games the Lions won
Rem INPUT: 10 game scores each consisting of a score
Rem for the Lions and a score for the opponent.
Rem OUTPUT: The scores and number of games the Lions won
Cls
Rem Initialize counters for games won and games played
A gamesPlayed=0
gamesWon = 0
Rem Header for scores
Print “Lions score”,”Opponent’s score”
Rem Enter a game score
L1: lions = Val(InputBox(“Enter a score:”))
opponent=Val(InputBox(“Enter score:”))
Print lions, opponent
Rem Find out who won this game
If lions opponent Then
B gamesWon = gamesWon + 1
End If
gamesPlayed = gamesPlayed + 1
C If gamesPlayed 10 Then
D GoTo L1
End If
Rem Display output
E Print “The Lions record for May is: “gamesWon;”-”;gamesPlayed

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6.6 Sentinels
Programs normally require the user to be able to input a different number of data items each time the
program is run. For example, the user may want to average all the grades for an exam for two different
classes that each has a different number of students. If a program always processed the same number of
data items, you would have to write a separate program for each different class size. The program would
be more effective if it were able to ask the user after each piece of data is entered and processed if there
is more data to be entered. Depending on the user’s response, the program will either process more data
or proceed with the computation that follows the input of all the data items. Regardless of the number
of pieces of data for a particular run of the program, the same program will always be used.
To make this process more efficient, we often use a sentinel. A sentinel is a special data value entered
by the user to signal the end of the valid input. A program that uses a sentinel tests each value that is
input to see if it is the value that signals that all the input data has been entered.

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To implement a sentinel, we add an If statement following the InputBox() line. The If statement is
designed to test a condition that asks whether or not the value just entered was the signal to end the
input operation. In case the value is not a signal to end the input operation, the program will know there
is a piece of data to process. When the user enters the sentinel, the program will know to discontinue
the processing of data. After determining that all the data has been entered, program control is then
transferred to the statement that is designed to do any summary computation or terminate the program.
A sentinel has the property that it is not a value that will ever be found in the user’s list of input values.
For example, if the user is entering grades with a range of 0-100, then any negative number or integer
greater than 100 could be used as a sentinel. If one attempted to use 38 as a sentinel, there is a chance
that the data could include that value. In such a case, the program would terminate when 38 was entered
rather than when all the data had been entered. If the input involves names, a string such as “END”
could possibly be a sentinel. The value of the sentinel is chosen by the programmer and is conveyed to
the user in the prompt message for the InputBox() command.
Example 6‑3. Write a program that allows a user to input the grades for as many students as he/she
likes. Output a list of the grades. Calculate and display the average of all the grades. Use a sentinel to
end the user’s input.
SAMPLE OUTPUT:
Grade entered: 86
Grade entered: 77
Grade entered: 94
Grade entered: 91
Grade entered: 83
The average grade is 86.2

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SOLUTION:
Rem Program allows a user to input the grades for any number of
Rem students. The program calculates and displays the average of
Rem the grades
Rem INPUT: Arbitrary number of grades and sentinel value
Rem OUTPUT: Each grade and the average of all the grades
Cls
Rem Initialize num (number of grades) and
Rem total (sum of all the grades) since the average will
Rem be total / num after all input values are entered
total = 0
num = 0
Rem Input
A L1: grade = Val(InputBox(“Enter grade (or -999 to end):”))
B If grade = -999 Then ‘ -999 is a sentinel
C GoTo L2
End If
Rem Process
Print “Grade entered: “; grade
D total = total + grade
E num = num + 1
Rem Repeat
F GoTo L1
Rem User entered -999 so finish program
L2: ave = total / num
Rem Display output
Print “The average grade is “; Format(ave, “standard”)

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COMMENTS: Notice in A that the program tells the user what value to enter when he/she is done
inputting data. There is no way the user can guess the sentinel, so the program needs to include that
information. In this case the value -999 is indicated as the sentinel. When a value is entered, it is
compared to -999. If the input value is not -999, grade is processed in D and E. The GoTo statement
in F then causes the program to transfer control to the statement with the line label L1 where the user
is asked to enter another grade. This is an unconditional transfer. When the user finally enters –999,
the condition B is true so the program transfers control to the statement with the line label L2 where
the average of the grades is calculated. The program then continues to the end. The transfer of control
to L2 is a conditional transfer since it only happens when the sentinel is entered making the condition
grade = -999 true.
When using a sentinel in your programs, it is important to choose a sentinel that is not a possible input
value. It is equally important to tell the user what the sentinel is.
6.7 Prompt and Echo
In a program, when we prompt users to enter data for the program to process, we should make an effort
to be sure that the input data is correct before we process it. Often, users unintentionally enter incorrect
data. For example, a typing error is not uncommon when entering data. If a user inputs data that is
incorrect in value, the program may run but produce an incorrect answer. To deal with this important
problem, we introduce a coding convention called prompt and echo.
Prompt and echo is a coding convention that assures as best as possible that the user has entered correct
data when prompted for input. Each time a user is prompted and inputs a piece of data, the data is
immediately displayed on the screen and the user is asked if it is correct. If the user answers that the
given data is correct, the program continues and processes the given data. If the user answers that the
data is incorrect, the program ignores the incorrect data and prompts the user again for a value. Only
after the user has confirmed that the data entered is a correct value does the program continue and
process the data.
Example 6‑4. Write a program that computes a bank account balance after a transaction has been
made. Have the user input the account’s previous balance, the transaction code, and the amount of the
transaction. The transaction code can be either a “D” for deposit or a “W” for withdrawal. Use the prompt
and echo convention to check the user’s input. Allow the user to process more than one transaction.
SOLUTION: The solution to this problem will have several parts that will be more easily understood if
they are dealt with separately. The first part of the program asks the user to enter the account’s previous
balance and uses the prompt and echo technique to check that the input is correct. The code in Part 1
shows this part of the program.

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Rem Program computes a bank account balance
Rem after a transaction has been made.
Rem INPUT: Balance, transaction code and amount of transaction
Rem OUTPUT: The final balance
Cls
A L1: balance = Val(InputBox(“Enter current balance.”))
Rem Prompt and echo (check if data is correct)
B p1 = “You entered “ balance “. Is this correct? (Y/N)”
C answer = InputBox(p1)
D If (answer = “N”) Or (answer = “n”) Then
E GoTo L1
End If
Part 1
In A, the user is prompted for the current balance which is a numeric value. Consequently, the Val()
built-in-function is used with InputBox(). When the user enters the balance, the program creates a
prompt (B) by concatenating text and the value just entered. The -operator merely joins the strings
“You entered “, a string version of balance, and the string “Is this correct? (Y/N)” to form a single string
p1. The numeric value of balance is converted to a string of symbols before the concatenation so that all
the parts of the statement are strings. In C, the program displays p1 as the prompt (thus echoing the data)
and asks the user if the input data is correct. If the user responds with a negative answer (“N” or “n”),
the GoTo statement in E sends the program control to the line labeled L1, causing the input process to
begin again for the variable balance. If the user responds to the question with anything other than “N”
or “n,” the program assumes that the input data is correct and continues to the next part of the program.
Notice that the condition in D allows the user to enter either a capital letter or a lowercase letter. Since
capital letters and lowercase letters have different ASCII-8 values, using Or avoids confusion by allowing
the user to enter either “n” or “N.” Otherwise, entering “n” when the condition only checked for “N”
would make the condition false and the user would be required to reenter a correct value.
The second part of the program processes the user’s deposits and/or withdrawals. This section of the
program inputs two values that indicate the type of transaction (code) and the amount involved (amount).
After entering this data, a prompt and echo is used to determine if the values are correct. The code in
Part 2 shows this code.

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Rem Data is correct. Prompt for more data.
F L2: code = InputBox(“Enter D for deposit or W for withdrawal.”)
G amount = Val(InputBox(“Enter amount.”))
Rem Prompt and echo (check if data is correct)
H p2 = “You entered “ code “ and “ amount “.”
p3 = “Is this code and amount correct? (Y/N)”
answer = InputBox(p2 p3)
If (answer = “N”) Or (answer = “n”) Then
I GoTo L2
End If
Part 2
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The user is prompted for the code and the amount of the transaction (F and G). The prompt and echo
convention begins at H as a string of words and a numeric value represented as symbols is constructed
to form a prompt for the InputBox() command. This prompt is fairly long so it is built by concatenating
the values of the string variables p2 and p3 with a string conversion of the numeric values code and
amount. Again, the user is asked if the data is correct. If the input data is not correct, the GoTo statement
in I sends the program to the line (F) labeled L2. The input process for a code and an amount is then
repeated. If the user responds with anything other than “N” or “n,” the input data is processed.
The third part of the program performs calculations with the data. The output is then displayed. The
code in Part 3 shows how this is done.
Rem Data is correct. Calculate balance.
J If (code = “D”) Or (code = “d”) Then
balance = balance + amount
K ElseIf (code = “W”) Or (code = “w”) Then
balance = balance – amount
Else
L Print “Incorrect Code Value”
End If
Rem Display output
Cls
M Print “The new balance is “ ; Format(balance, “currency”)
Part 3
The code in this section contains a multi-case If block that matches the input transaction code to the
appropriate calculation. In J, code is tested to see if is equal to “D” or “d.” If the condition is true, the
transaction is a deposit, and the transaction amount is added to the balance. In K, code is tested to see
if the transaction is a withdrawal. In that case, the transaction amount is subtracted from the balance.
The code in L guarantees that if an invalid code is entered, the balance will not be changed. In M the
new balance of the account is displayed.

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You might ask why code such as
If (code = “D”) Or (code = “d”) Then
A balance = balance + amount
Else
B balance = balance – amount
End If
was not used. In fact, this simple If…Then…Else…End If could have been used. As a matter of style
and for the purposes of promoting correctness, this simpler code was not used because it really says if
code is equal to “D” or “d,” do A; and if code has any other value, do B. When we know that code will
have fixed values, it is better programming practice to make the program guarantee the correct value is
being processed. If an additional operation is added, it will be easier to add the code. If the ElseIf is not
used and another operation is added,
balance = balance – amount
would be executed for both a withdrawal and the additional operation. This may well not be the processing
the new operation needs.
On Your Own
1. Simulate the code of Example 6-1 parts 1-3 and process the following data:
Previous Balance = 135.78
Transaction 1: withdraw 55.67
Transaction 2: deposit 76.88
Transaction 3: deposit 335.67
Transaction 4: withdraw 66.34

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6.8 User Interrogation Technique
The final part of the program offers the user the option to process another transaction. This technique
is often used to verify that a user really wants to exit a program. The code in Part 4 shows this.
Rem Interrogate user
M answer = InputBox(“Process another transaction? (Y/N)”)
N If (answer = “Y”) Or (answer = “y”) Then
O GoTo L2
End If
Rem display output
P Cls
Print “Final balance: “; Format(balance, “currency”); “ Thank you!”
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119
Branching
In this section, the program asks the user in M if there is another transaction to process. If the user
answers positively, the GoTo statement in O causes the program to continue execution at the line labeled
L2 (F in Part 2). Otherwise, the program continues to execute at P and displays a message indicating
the program is ending. Notice in the condition in N that the program again allows the user to enter
upper or lower case letters.
On Your Own
1. Enter the code of Example 6-4 parts 1-4 and run the program with data you create.
1. Use conditional branching to write a program that displays the list of integers from 30 to 50
along with their squares. Be sure to include text to make the output clear. For instance, your
program’s output may look something like this:
30 squared equals 900

Hint: Initialize a variable to 30. Rather than using an InputBox function, you can just increment
by one to get the next number to square.
2. Use conditional branching to write a program that counts backwards and displays the
numbers from 10 to 0.
3. Write a program that inputs a series of grades and outputs each grade after it is entered.
After each grade is processed, ask the user if there are any more grades to be entered. At the
end, output the highest grade.
4. Write a program that inputs the ages of several people. Calculate the average age of the
people. Be sure to implement prompt and echo when acquiring the data needed.
5. The mean of a set of N numbers is 62. Enter the N numbers and determine how many are
larger than the mean. Use conditional branching to test how many numbers have been
processed so that the program terminates after processing N numbers.
6. Enter the monthly total of sales for Fine Wheels. Sum and print the value of all the sales.
Also calculate the most expensive car price for this month.
7. Enter N names together with the two symbol state code for the person’s home state. Output
any name with state code NJ, PA, or WA. Count and output the number of names that
satisfy the condition.

120
Branching
8. Enter N measurements of weekly rainfall. Use conditional branching with a sentinel to sum
and print the total of all the measurements. After entering the measurements, compute the
average weekly rainfall for the values given.
9. Suppose the mean (m) of a set of number is 86 and the standard deviation (stDev) is 16. For
any value input determine its grade using the following table:
Less Than Greater Than Or Equal Grade
m – 2 * stDev Not Passing
m - .75 * stDev m – 2 * stdev C
m + stDev m - .75 * stDev B
m + stDev A
Using conditional branching determine the result for any number of test takers using a sentinel
of -333 to terminate the processing
Send us your CV on

121
For .. Next Loops
7 For .. Next Loops
In the previous chapter about branching, we studied programs that repeated certain sections of code.
Using conditional branching to repeat code is one form of looping or repetition. Looping is an important
programming structure that allows a fixed sequence of instructions to be executed under program control
as many times as needed. At each repetition of the code, although the instructions may be the same,
the instructions act upon variables whose values may be different. In this section, we discuss a form of
looping or repetition in which the number of times the loop repeats is determined when the loop begins
and the control of looping is built into the syntax rather than programmer written conditions.
The program shown in Figure 7-1 recaps the sales records for the ten most popular items during the last
sales period. The input for each item consists of the name of the item, the number of units of this item
sold, and the cost for one unit of the item. The total revenue for each item includes a 25% markup. The
computation for each item is the same. By using loops the code need only be written once and used as
many times as needed.

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7.1 The For .. Next Loop
In the section on conditional branching, we saw that to repeat a block of code a fixed number of times
we needed to initialize a counter, execute the block of code, increment and test the counter to see if the
block of code is to be repeated, and then transfer control to the first statement in the block of code if it
needs to be repeated. If the block of code is to be repeated, we execute it and repeat the incrementation,
testing, and transfer steps until we have repeated the block of code the required number of times. When
the required number of repetitions are completed, the program continues on. In this section we want to
see how all this bookkeeping is built into BASIC syntax.

122
For .. Next Loops
When we know exactly how many times a block of code should be repeated, we can use a For .. Next
loop as shown in the syntax box instead of conditional branching as we saw in the previous chapter.
SYNTAX
For..Next Loop
For variable = num1 To num2
Actions to be repeated-body of the loop
Next variable
Note: variable is any variable name.
EXAMPLE: For I = 3 To 5
X = InputBox(“Enter a city name:”)
Print X
Next I
Scan for free
Agilent iPhone
Apps or visit
qrs.ly/po2Opli

123
For .. Next Loops
Before examining the semantics of the For .. Next loop, we describe the syntax for this construct. A For ..
Next loop always contains a For marker and a Next marker. The For marker indicates the beginning of
the loop. Following the For marker is a variable which is referred to as a control variable to indicate
its role in determining how many times the body of the loop will be repeated. We use variable as a
representative for any variable name the programmer chooses to use in its place. The control variable
is followed by an equal sign. On the right of the equal sign are two numeric values separated by the To
marker. The values num1 and num2 can be numbers, defined numeric variables, or numeric expressions.
In most cases num1 is less than num2. The body of the loop, which is the code to be repeated, appears
next. Following the body of the loop is the Next marker followed by the same variable referred to in
the For statement.
Now we can use our understanding of this syntax to discuss the semantics of a For .. Next loop. When
the loop begins executing, the For statement specifies that the control variable should be initialized to
num1. The number range determined by the two values num1 and num2 following the equal sign marker
is first checked by testing the condition where variable now has the value num1:
variable = num2
If the condition is true, the body of the loop is executed with variable having its initial value. After the
body of the loop has been executed and the Next statement is reached, the Next statement causes several
actions, the first of which is to increment variable by 1. The new value of variable is compared with the
value of num2 by again checking the condition
variable = num2
If the new value of the control variable is still less than or equal to the value of num2, the condition is true
and the program control is transferred to the first statement in the body of the loop and the body of the
loop again is executed. When the Next statement is encountered again, the increment and test procedure
is repeated so that the program knows whether or not to transfer to the beginning of the body of the
loop to repeat the body of the loop another time. When the control variable is incremented resulting in
the new value being greater than num2, the program control is passed to the statement following the
Next statement because the condition will evaluate to false. In total the body of the loop will execute
num2 – num1 + 1
times before the condition num1 = num2 becomes false provided initially
num1 = num2.

124
For .. Next Loops
The values num1, num1 + 1, … , num2 are called the range of the control variable. Figure 7-2 shows
an example block of code that contains a For .. Next loop that will have the code (C and D) that is the
body of the loop executed three times.
A sumOfXes = 0
B For I = 1 To 3
C x = Val(InputBox(“Enter a number:”))
D sumOfXes = sumOfXes + x
E Next I
F Print “Sum of values:”;sumOfXes
Figure 7‑2: Example For .. Next Loop
In Figure 7-2, statement A initializes the accumulator variable sumOfXes to zero. Statement B marks
the beginning of the For .. Next loop and initializes the counter I to 1. This line also specifies that the
range of the counter will be from 1 to 3. Since the initial value assigned to I is less than or equal 3, the
body of the loop is executed next. At C a number is input. Statement D adds the inputted number to the
current value of sumOfXes. Statement E marks the end of the body of the loop and increments I by one.
If I does not exceed 3, the loop repeats beginning at C. If I is greater than three, the program continues
with F and displays the value of sumOfXes.
A complete trace of the execution of this program will help clarify what happens in a For .. Next loop.
The trace shows the values of the variables after a statement has been executed. The complete trace is
found in Table 7-1. (When you come to the bottom of the pair of columns labeled “Value of variables,”
move to the next column with this label and follow the continued execution of the program.)
Assume the input values are X1, X2, and X3.
Statement Value of Variables Statement Value of Variables
SumOfXes I x SumOfXes I x
A 0 D X1+X2 2 X2
B 0 1 E X1+X2 3 X2
C 0 1 X1 C X1+X2 3 X3
D X1 1 X1 D X1+X2+X3 3 X3
E X1 2 X1 E X1+X2+X3 4 X3
C X1 2 X2 F X1+X2+X3 4 X3
Table 7‑1: Trace of the Program in Figure 7-2

125
For .. Next Loops
The actions of a For .. Next loop are similar to conditional branching which uses a GoTo statement and
a counter incrementing and testing step to repeat sections of code. See Figure 7-3 for two equivalent
programs that perform looping. The first program loops by using conditional branching with a GoTo
statement within an If block. The second program loops by using a For .. Next loop.
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126
For .. Next Loops
Rem Using conditional branching Rem Using a For .. Next loop,
Rem this program displays five Rem this program displays five
Rem names input by the user. Rem names input by the user.
Rem INPUT: Five names Rem INPUT: Five names
Rem OUTPUT: Five names Rem OUTPUT: Five names
Cls Cls
Rem Initialize i Rem Loop to input/display names
A I = 1 F For I = 1 To 5
L1: nam = InputBox(“Enter a name:”) nam = InputBox(“Name:”)
Print “The name is “; nam Print “The name is “; nam
Rem Increment I and decide to G Next I
Rem input another name or end
B I = I + 1
C If I = 5 Then
D GoTo L1
E End If
Figure 7‑3: Equivalent Programs that Demonstrate Two Forms of Looping
Both of the programs in Figure 7-3 produce the output shown in Figure 7-4 with input Cosmo, Elaine,
George, Jerry, and Norman.
The name is Cosmo
The name is Elaine
The name is George
The name is Jerry
The name is Norman
Figure 7-4: Output of the Programs in Figure 7-3
If we compare the two programs in Figure 7-3, we see that they perform the same task, but one program
is much simpler than the other. By using a For .. Next loop in the second program, we reduce the
length of the program and make the structure of the program clearer. In Figure 7-3, F in the second
program replaces and performs the same tasks as both A and C in the first program. Remember the
initial statement of a For .. Next both initializes the control variable and tests to see if the body of the
loop should be executed. Also, G in the second program replaces and performs the same tasks as B,
C, D and E in the first program. These two programs demonstrate well the advantages of a For .. Next
loop. This syntax is a case of encapsulation. The initialization, incrementation, testing, and transfer are
packaged or encapsulated in the For and the Next statements.

127
For .. Next Loops
For another example of a For .. Next loop, see Figure 7-5.
For K = 2 To 10
sq = K * K
Print “The square of”; K; “ = “;sq
Next K
Figure 7‑5: Example For .. Next Loop
In Figure 7-5 notice the spacing conventions used within a For .. Next loop. The body of the loop should
be indented to make it clear what instructions are repeatedly executed. Also notice in the example that
the number range assigned to the control variable of the loop need not begin with zero or one. Any
integer numbers can be used as values for num1 and num2. Variables representing decimal values can
also be used as values for the loop starting and ending values. Notice also that in Figure 7-5 that the
control variable value can be accessed and used for calculations within the body of the loop. However,
the control variable should never be altered within the body of the loop!
Example 7‑1. Write a program that uses a For .. Next loop to calculate and display the sum of the
numbers from 1 to 10.
SOLUTION:
Rem Use a For .. Next loop to display
Rem the sum of the numbers from 1 to 10
Rem OUTPUT: The sum of 1, 2,…,10
Cls
Rem Initialize total
total = 0
Rem Loop to calculate total
For I = 1 To 10
total = total + I
Next I
Rem Display output
Print “The sum of 1 to 10 =”; total

128
For .. Next Loops
COMMENTS: If we think about how we would code this program using conditional branching, we
should see that using a For .. Next loop is easier and more convenient. The program is easy to code,
read and follow, and it does not seem to “jump around” as with GoTo statements.
On Your Own
1. Use a For .. Next loop to write a program that displays all the numbers from 10 to 20.
2. Use a For .. Next loop to write a program that displays the product of the integers in
the range 18 to 41. Output the total product of those numbers. To calculate the product,
initialize a variable outside the loop to have a value of one.
7.2 The Step Parameter
In the For .. Next loops that we just studied, the control variable in the loop was always incremented by
one when the Next statement is encountered. In some situations, we may wish to increment the control
variable by a different value. To do this, we can use the extension of the syntax for the For statement to
include the Step marker.

129
For .. Next Loops
SYNTAX
For .. Next With Step
For variable = num1 To num2 Step increment
Code to repeat-body of the loop
Next variable
EXAMPLE: For I = 1 To 30 Step 3
Print I, I^2, I^3
Next I
Some of the output:
I I^2 I^3
1 1 1
4 16 64
7 49 343
The Step marker and an increment value follow the number range in the first line of a For .. Next loop.
Following the keyword Step is a value or expression that specifies the amount by which to increment
the control variable in the loop. This value can be any negative or positive value, a variable representing
a numeric value, or an expression to be evaluated when the For statement is executed. When the Step
parameter is used with a For .. Next loop, the loop executes as normal except that the control variable
is incremented when the Next statement is encountered by the value specified by the increment in the
Step option. If the increment value is positive, the number range must be from low to high (num1 =
num2) as it was previously. If the increment value is negative, the specified number range (num1 To
num2) must be from high to low (num1 = num2) so that the counter will be within the range as it is
decremented. The test will be
variable = num2
with a negative increment value rather than
variable = num2
with a positive increment value. For a negative increment value, the loop terminates when
variable num2.
Keep in mind that if the Step parameter is not used, the counter is incremented by one, the default value.
If the increment is negative and num1= num2, the body of the loop will not be executed even once!

130
For .. Next Loops
A p=0 ‘initializes an accumulator
B For I = 15 To 5 Step -4
C p = p + I
D Print p
E Next I
F Print “Final sum =”; p
Figure 7‑6: For .. Next loop with Negative Increment (Step Size)
In the program in Figure 7-6 the increment is a negative integer. Thus, the number range specified is
from 15 to 5 rather than from 5 to 15. The values assigned to I will be 15, 11, 7, and 3. Remember that
when a negative counter is specified by the Step parameter, the number range must go from high to low
so that the counter may be decremented rather than incremented. The idea is clearer when you trace the
execution of this code as shown in Table 7-2. (Read this table following the directions given for Table 7-1.)

Statement Variables Statement Variables
p I p I
A 0 D 26 11
B 0 15 E 26 7
C 15 15 C 33 7
D 15 15 D 33 7
E 15 11 E 33 3
C 26 11 F 33 3
Table 7‑2: Trace of program in Figure 7‑6
The program Figure 7‑6: For .. Next loop with Negative Increment (Step Size)7-6 prints the values of p
in the body of the loop while the loop parameter takes on the values 15, 11, and 7. Notice that the last
value for I when p is printed is 7 and not 5, even though the number range goes to 5. Since the decrement
specified is minus four, only every fourth number will be assigned to I. When the control variable has
reached 7, it is decremented again by four giving a value of 3. At this point, the control variable is less
than 5, and the program continues execution at the first statement following the end of the loop.
On Your Own
1. Write a program to display the odd integers between 7 and 34 in increasing order. Repeat
the problem but display the integers in decreasing order.

131
For .. Next Loops
2. Write a program that computes the product of the even integers in the range N to 60. You
can test if an integer is even by the condition
I mod 2 = 0.
What if N 60?
3. Explain why the following For..Next loops are invalid.
(a) For k = 5 To 10
Print 1 / k
Next x
(b) For n 30 To 15 Step -4
p = p * n
Next n
Example 7‑2. Using a For .. Next loop with a Step parameter, write a program that calculates and displays
the product of all the odd numbers from 1 to 19.
OUTPUT:
The product of all the odd
numbers from 1 to 19 is 654729075
Brain power

132
For .. Next Loops
SOLUTION:
Rem Display the product of all the odd numbers
Rem from 1 to 19
Rem OUTPUT: Text with the product of 1*3* … * 19
Cls
Rem Initialize
product = 1 ‘accumulator for multiplication
Rem Loop to calculate product
For I = 1 To 19 Step 2
product = product * I
Next I
Rem Output
Print “The product of all the odd”
Print “numbers from 1 to 19 is”; product
On Your Own
1. Use one For .. Next loop with the Step parameter to write a program that displays the
numbers from 20 to 2 (in that order) on the screen. Also display the sum of the squares of
those numbers.
2. Input a positive integer N. Compute and print the product of all positive even integers less
than or equal to N. For example, if N = 13, the output is
2· 4 · 6 · 8 · 10 · 12 = 46080
3. Write a program that computes the sum of all the odd integers between N and 60. The value
of N is supplied by the user.
7.3 Program Applications
The BASIC For .. Next loop with the Step parameter can be very helpful in many applications. We can
find the interest earned by an investment over a period of time or the balance between economic supply
and demand.
Example 7‑3. The future value of an investment is the value of that investment after earned interest has
been added at the end of each compounding period. Prepare a table that shows the future value of $100
after 1, 2, 3 and 4 years when interest is earned at each of the rates 3%, 3.25%, 3.5%, …, and 6% and
paid at the end of the year.

133
For .. Next Loops
OUTPUT:
Rate Year 1 Year 2 Year 3 Year 4
3.00% 103.00 106.09 109.27 112.55
3.25% 103.25 106.61 110.07 113.65
3.50% 103.50 107.12 110.87 114.75
3.75% 103.75 107.64 111.68 115.87
4.00% 104.00 108.16 112.49 116.99
4.25% 104.25 108.68 113.30 118.11
4.50% 104.50 109.20 114.12 119.25
4.75% 104.75 109.73 114.94 120.40
5.00% 105.00 110.25 115.76 121.55
5.25% 105.25 110.78 116.59 122.71
5.50% 105.50 111.30 117.42 123.88
5.75% 105.75 111.83 118.26 125.06
6.00% 106.00 112.36 119.10 126.25
SOLUTION:
Rem Calculate and display the future value of $100 at yearly intervals
Rem with compounding at interest rates between 3% and 6%
Rem with .0025% increments.
Rem OUTPUT: Table of future values
Cls
Rem Display the table header
Print “Rate Year 1 Year 2 Year 3 Year 4”
Rem Calculate future values as interest rate
Rem varies from 3% to 6% at 0.25% increments
A For interest = .03 To .06 Step 0.0025
year1 = 100 * (1 + interest)
year2 = 100 * (1 + interest) ^ 2
year3 = 100 * (1 + interest) ^ 3
year4 = 100 * (1 + interest) ^ 4
B Print Format(interest, “percent”);
C Print Format(year1, “ 000.00”);
D Print Format(year2, “ 000.00”);
E Print Format(year3, “ 000.00”);
F Print Format(year4, “ 000.00”)
Next interest

134
For .. Next Loops
COMMENTS: In the program, the For .. Next loop beginning in A calculates the future values of $100
for four years. The figures are calculated for different interest rates each time the loop is executed. In A,
the Step parameter with the For .. Next loop increments the interest rate by 0.0025 (0.25%) each time
the loop is repeated. In B, the interest rate is displayed using the built-in percent formatting pattern.
In lines C through F spaces are used in the formatting pattern so the displayed values line up with the
headings. Note that each Print command ends in a semi-colon except the last one. This causes the
interest rate and the four values for the different years to be printed on one line one after another. After
the fourth value is printed, the printer advances to the beginning of the next line. Each iteration of the
loop prints one row of the table.
Another application of For .. Next loops is in the economic theory of supply and demand. With the
use of For .. Next loops and the Step parameter, we can write a BASIC programs to find the point of
equilibrium between a supply curve and a demand curve. In economics the equilibrium point is the
value at which the supply curve intersects the demand curve. Supply curves are always increasing
functions while demand curves are always decreasing functions. With the price of a product less than
the equilibrium price, the model implies that the demand is greater than the supply. A price higher than
the equilibrium price indicates the supply exceeds the demand for the product.
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135
For .. Next Loops
Example 7‑4. The supply and demand curves for gyzmos for the Ark Gyzmo Co. have been determined
as the following functions:
S(p) = -1 + 0.10 p2
D(p) = 1 – 0.04 p
Here S(p) is the supply curve which tells how many units are produced when the price per unit is p.
D(p) is the demand curve which tells how many units are wanted by the consumer at the price p. In
this example S(p) and D(p) are quantities of gyzmos and p is the price for one gyzmo. The graph in
Figure 7-7 shows the supply and demand curves for gyzmos. S(p) gives the number of gyzmos that are
being produced when the selling price is p. D(p) is the number of gyzmos that could be sold at price
p. As supply increases, the excess demand will decrease until the supply and demand are in balance at
the equilibrium point. Obviously, if the demand is higher than the supply, more suppliers will enter the
market to meet the demand. The price of the additional units produced will be lower as unmet demand
decreases.
0
1
2
3
4
5
6
7
8
9
0 1 2 3 4 5 6 7 8 9 10
price (dollars)
quantity
(1000s)
demand
curve
supply
curve
equilibrium point
Figure 7‑7: Supply and Demand Curves
Write a program that finds the first value for quantity and price (to the nearest penny) greater than
$4.00 for which the number of gyzmos supplied is greater than the number of gyzmos demanded by
the marketplace. Display in thousands how many gyzmos should be produced and what the price of
each gyzmo should be in order to approximate equilibrium. We see from graphing the functions that
the answer lies between 4 and 7 so we use those values in the For statement.
OUTPUT:
For equilibrium, 2,576 gyzmos should be
produced with a selling price of $5.98 each.

136
For .. Next Loops
SOLUTION:
Rem Find the equilibrium point for a given
Rem pair of supply and demand curves.
Rem OUTPUT: Number of gyzmos and the price to
Rem the nearest penny of a gyzmo at equilibrium price
Cls
Rem Find supply and demand at increasing prices
A For p = 4.0 To 7.0 Step 0.01
supply = -1 + 0.1 * p ^ 2
demand = 2 – 0.04 * p
B If supply = demand Then
price = p
GoTo L1
End If
Next p
Rem Display output
L1: Print “For equilibrium, “;
Print Format(supply * 1000, “0,000”);
Print “gyzmos should be”
Print “produced with a selling price of “;
Print Format(price, “currency”);
Print “each.”
COMMENTS: In the program the For .. Next loop beginning at A uses the price of a gyzmo as its
control variable, p. It begins with a price of $4.00 and has a step size of one penny. For each price, the
supply and demand are calculated using the equations given. The supply curve is always an increasing
function and the demand curve is always a decreasing function. In the If block at B, the value of the
supply function is compared to the value of the demand function. At the value of p for which the supply
value is greater than or equal to the demand value, the value of the equilibrium point has been passed
by at most 0.01 and the program transfers control out of the loop. If the supply value is less than the
demand, equilibrium has not yet been reached. In this case, the loop repeats with an increased price.
When the program finally does drop out of the loop, the current values of supply and p represent the
number of gyzmos and the price of a gyzmo at the approximation of the equilibrium point. From the
graph we drew in the analysis of the problem, we know that the equilibrium point will be found before
p has a value greater than 7.0. Thus we will not terminate the loop by having p take on a value greater
than 7.0 but by having the condition in B becoming true.

137
For .. Next Loops
7.4 Generalized Functionality
A very important use of For .. Next loops is to make a program become a solution for a class of
problems. For example, the simple program of summing a list of numbers could be programmed
for 10 values as shown in Figure 7-8.
Rem Sum 10 numbers
Rem INPUT: Ten numbers one at a time
Rem OUTPUT: The sum of the 10 numbers entered
sum = 0
For I = 1 To 10
num = Val(InputBox(“Enter a number”))
sum = sum + num
Next I
Rem Output sum
Print “The sum of 10 numbers = “;sum
Figure 7-8: Loop to Process 10 Values

138
For .. Next Loops
The problem with this program is obvious when someone asks for a program that sums 12 numbers, or
15 numbers, or 23 numbers, …. There is no point in writing a program for a fixed number of numbers
when the program can be written to handle any number of numbers. To write a more general program we
have to think of the For .. Next idea extended to include the ability to work for any number of numbers.
We do this in the program shown in Figure 7-9.
Rem Sum N numbers
Rem INPUT: The number of numbers N and each of the numbers
Rem OUTPUT: The sum of the N numbers entered
sum = 0 ‘initialize an accumulator
N = Val(InputBox(“Enter the number of numbers to process:”))
For I = 1 To N
num = Val(InputBox(“Enter a number”))
sum = sum + num
Next I
Rem Output sum
Print “The sum of “;N;”numbers = “;sum
Figure 7‑9: Loop to Process Any Number of Values
The program now will work regardless of the number of numbers that need to be processed. Granted the
user will have to count the number of data values to be processed to supply the correct value when the
InputBox() command prompts for that value. This does seem to be a small price to pay for the greater
flexibility. Programs are usually designed and written to handle any number of input values since a For
loop does not care if the body of the code is repeated 10 or 20 or 200 times.
7.5 Nested Loops
The body of a loop can contain any sequence of commands including another For .. Next loop. The code
in this case will look something like:
For I = num1 To num2
…
For J = num3 To num4
Next J
….
Next I
Figure 7‑10: Model of a Nested Loop

139
For .. Next Loops
The loop with I as a control variable is called the outer loop. The loop with J as a control variable is
called an inner loop. The only restriction on an inner loop is that the variable name used as a control
variable cannot be the same as the variable name of the counter variable of the outer loop and the Next
statement of the inner loop must occur before the Next statement of the loop containing it.
As an example it is known that the sum of N odd numbers starting with 1 gives a value of N^2. In Figure
7-11, we verify this for all values less than or equal to an input value N by adding up the odd numbers
1, 3, … , 2*I – 1 for each value of I in the range 1, 2, …, N.
A
B
C
D
E
F
G
N = Val(InputBox(“Enter an Upper Bound”))
Rem Print header for columns of values
Print “ I”,”Sum of odds less than I”
For I = 1 To N
sum = 0
For J = 1 To I
sum = sum + 2 * (J – 1) + 1
Next J
Print I, sum
Next I
Figure 7‑11: Computing N^2 as a Sum of Consecutive Odd Integers
Tracing the program for N = 3 will give an insight into how the nesting of the loops work.
Statement Variables Statement Variables Statement Variables
I J sum I J sum I J sum
A 1 D 2 1 1 E 3 2 1
B 1 0 E 2 2 1 D 3 2 4
C 1 1 0 D 2 2 4 E 3 3 4
D 1 1 1 E 2 3 4 D 3 3 9
E 1 2 1 F 2 3 4 E 3 4 9
F 1 2 1 G 3 3 4 F 3 4 9
G 2 2 1 B 3 3 0 G 4 4 9
B 2 2 0 C 3 1 0
C 2 1 0 D 3 1 1
Figure 7‑12: Tracing Program in Figure 7-11

140
For .. Next Loops
1. Write a program to compute and display the sum of
100
9
9
5
4
4
3
3
2
2
1
+
+
+
+
+ 
Display the output with three decimal digits.
2. Input a pair of integers with the first representing the Kings’ score for a game and the
second representing the opposition’s score. For each input pair, determine which team won.
At the end, output the total number of wins and losses for the Kings. Suppose the Kings play
20 games in a season.
3. Ask the user to input the cost of tuition at a university this year. Suppose the tuition
increases by 5.2% per year for the next fifteen years. Using a For .. Next loop, calculate
the tuition costs for each of the next fifteen years. The output of your program may look
something like this:
The tuition in 2015 will be $00,000.00

4. A bank pays 5.6% interest on passbook savings. Suppose that on January 1, 2017, a savings
account contained $2,500. Interest is credited to the account on the first day of each month
on the balance of the account on the 15th of the previous month. On the 15th day of each
month the customer deposits an additional $250. Calculate and display the balance of the
account on the first day of each month for the next two years.
5. The Ark Gyzmo Co. produces the world’s finest gyzmos. Direct production costs per gyzmo
amount to $120. Secondary costs are $0.75N^2 per day where N is the number of gyzmos
produced that day. Gyzmos are sold for $212 each. Write a program that calculates the profit
for production levels that range from ten to thirty gyzmos per day.
6. The Board of the Huxville Symphony makes a list of all donors and the amount each has
given at the end of the fiscal year. Suppose there are N donors. Output a list of the names
and amounts given for each of the donors.

141
For .. Next Loops
7. Compound interest is calculated using the formula
interest = principal * (1 + rate) ^ years
Calculate the interest value for $100, $200, and $300 at the end of each of the next ten years
if the interest rate is 8%.
8. Write a program to find the average of any number of numbers. Each time the program is
run, the user should input the number of numbers to be entered.
9. For each integer N in the range 1 to 10, compute the sum of the squares of all the integers
less than or equal to N.
10.For each integer N in the range 10 to 15, compute the sum of all the odd integers less than
or equal to N.

142
Random Numbers
8 Random Numbers
Random numbers are used to implement simulation models and games of chance. For example, random
numbers can be used to simulate the tossing of a coin or the rolling of a pair of dice. BASIC provides a
built-in-function to generate random numbers that can be used in programs that randomly determine
the next event of a simulation or the next play of a game.
Gaming machines pay off if the picture on each of the spinning wheels ends up the same in the display
window at the end of the spin. Simulations of this game, often called a “one-armed bandit,” uses
random numbers and statistical distributions to determine what the final picture is on each wheel. The
programmer then checks to see if the pictures are the same on all three wheels to know if there is a
winner. The output in Figure 8-1 is the result of code that simulates a gaming device with three wheels.

5DQGRP1XPEHUV8VHGWR
*HQHUDWH$QLPDOV2Q:KHHOV
RQGLWLRQDO6WDWHPHQWV'HWHUPLQH
+RZ0DQ$QLPDOV0DWFK
7KHQXPEHURISODVLV
FRQWUROOHGEDORRS
Figure 8-1: One-Armed Bandit
8.1 The Rnd Function
The BASIC function to generate a random number is Rnd. The Rnd function returns a randomly selected
number between 0 and 1 (including 0 but not including 1). For instance, the following statement
randomNo = Rnd
assigns a number between 0 and 1 to the variable randomNo. Each time the Rnd function is executed in
a program, a number between 0 and 1 is produced. In most cases when a random number is generated,
it is assigned to a variable since every time Rnd is encountered in a program a different random number
is generated. For example, if we have the code
randomNo = Rnd

143
Random Numbers
and then the code
Print randomNo, Rnd
We will get two different values printed.
Example 8‑1. Using the Rnd function, write a program that generates 10 random numbers between 0
and 1.
SOLUTION:
Rem Generate 10 random numbers between 0 and 1
Rem OUTPUT: 10 random numbers
Cls
For I = 1 To 10
Print Rnd
Next I
OUTPUT:
0.7055475
0.533424
0.5795186
0.2895625
0.301948
0.7747401
1.401764E-02
0.7607236
0.81449
0.7090379
COMMENTS: In the program, we use a For .. Next loop to call the Rnd function ten times. Each
time the Rnd function is called, a different random number between 0 and 1 is produced. The format
1.401764E –02 is scientific notation to represent 0.01401764. Normally, computers represent numbers
so that the first significant digit of a number is a non-zero digit. A number like 1.401764E-02 is the
computer representation for 1.4014764 * 10^(-2) or 0.014014764.
SYNTAX
Rnd Function
Rnd returns a random number from [0, 1).

144
Random Numbers
8.2 Using Randomize
Though the previous program produces ten different random numbers, the same ten numbers are
produced in the same sequence each time we start and run the program. This program behavior would
lead the user quickly to learn an optimal strategy for a program or game using random numbers to
determine outcomes. To write a program to play a game or simulate a sequence of events, it is important
that each time the program runs the sequence of events is different. Otherwise, the user will learn how to
win the game by just remembering what the schedule of the events is. Using random numbers with the
Rnd function begins generating a sequence of random numbers when BASIC supplies an initial value to
the code of the Rnd function. If the same starting value is supplied every time the Rnd function starts
generating a sequence of random numbers, the sequence of random numbers will always be the same.
This description of how the Rnd function gets started tells us how we can generate different sequences
of random numbers. We just need to supply the Rnd function with a different starting value each time
a program begins to execute. In BASIC this is done by using the key word Randomize at the start of
the program. When a program includes the Randomize command, a different starting value is used
each time the program executes. In each instance that Rnd is used, the numbers generated will have the
same properties but if the program includes Randomize, the sequence of numbers will be comprised of
different numbers. The starting value for Rnd is called a seed.

145
Random Numbers
When Randomize is executed, the program interprets the contents of some memory location as a number
and sets the random number seed to that value. The function Rnd then uses the seed as a starting value.
Different seeds will give different starting values and different sequences of random numbers. The entire
process of finding an initial value for Rnd is called seeding the random number generator.
Figure 8-2 shows the output from two more executions of a program like the one in Example 8-1 but
including Randomize before Cls. Notice that the executions produce different sequences of numbers.
Both sequences of numbers will have the same properties but each is produced using a different seed.
Sample output #1 Sample output #2
0.2620508 0.3679773
0.4732891 0.1242596
0.9317983 0.0726369
0.7170985 1.333261E-02
0.566215 0.5212626
0.3413142 0.9449214
0.2361704 1.909882E-02
0.3286405 0.1986051
0.4076144 0.1414706
3.903973E-02 0.8062211
Figure 8-2: Random Numbers Generated Using Randomize
On Your Own
1. Write a program to display and add five random numbers between 0 and 1. Display the sum
of the five numbers. Run the program three times. Use the Randomize command so that
each time you run the program, you should get a different result.
2. What is the range of numbers generated by 17*Rnd, 21*Rnd, and 52*Rnd?
3. Write a program to show that there are different values generated each time Rnd is called in
a program. The program should have just two lines of code:
X = Rnd
Print X, Rnd
SYNTAX
Randomize
Randomize generates a seed for Rnd. Each time
the program is executed a different seed is found.

146
Random Numbers
8.3 Coin Tossing
Random numbers can be used to simulate the tossing of a coin. When a coin is tossed, there are two
possible results: heads or tails. Each result has a 50% chance of occurring, providing the coin is fair, i.e.
each outcome is equally likely to occur. To simulate a coin toss, we want to use the Rnd function. Since
the Rnd function produces numbers between 0 and 1, we must decide which numbers generated by Rnd
will represent flipping a head and which numbers will represent flipping a tail. Since the two events are
equally likely and all numbers between 0 and 1 are equally likely to result from the Rnd function, we
need to have half the numbers possible to represent flipping a head and the other half of the numbers
possible to represent flipping a tail. Thus, since the interval [0, 0.5) is half of [0, 1), we can assign the
values of Rnd less than 0.5 to mean flipping a head and the numbers greater than or equal to 0.5 to
mean flipping a tail. (See Figure 8-3.)
Heads Tails
0 .5 1
Figure 8‑3: Number Representation of Heads and Tails
Example 8-2. Write a program that simulates the tossing of a fair coin ten times. The outcome should
indicate the result of each toss.
SOLUTION:
Rem Simulate the tossing of a coin and
Rem display the result of each toss.
Rem OUTPUT: Text with the results of the coin toss
A Randomize
Cls
B For I = 1 To 10
C flip = Rnd
D Print “Flip “ I “: “; ‘concatenate for style
If flip 0.5 Then
Print “The coin came up heads.”
Else
Print “The coin came up tails.”
End If
Next I

147
Random Numbers
OUTPUT:
Flip 1: The coin came up tails.
Flip 3: The coin came up heads.
COMMENTS: Because the program includes the Randomize (A) command, each time the program is
run a different set of 10 random numbers will be generated. The sequence of outputs shown may never
show up again! The Rnd function in C of the program generates a number between 0 and 1 (excluding
1) and assigns that number to flip. The For .. Next loop beginning in A repeats the loop ten times for
ten tosses of the coin. The string concatenation in D removes the following space when I is printed as a
number. Try this print statement with a semicolon replacing “” to see the difference.
+ in + + ity
the of th + - c
- ste

148
Random Numbers
On Your Own
1. Write a program that simulates 100 tosses of a coin. Record and display the number of
heads and the number of tails that resulted. Display the final count. Run the program 10
times and compare the different outputs.
8.4 Tossing a Biased Coin
Suppose that we toss a biased coin that comes up heads 35% of the time and tails 65% of the time. To
simulate a toss of this coin, we must assign 35% of the values that could be produced by Rnd to represent
heads and 65% of the numbers that could be produced by Rnd to represent tails. Therefore, let us say
that any random number generated that is less than 0.35 will represent flipping a head, and the random
numbers greater than or equal to 0.35 will represent the event of flipping a tail. (See Figure 8-4.)
Heads Tails
0 .35 1.0
Figure 8-4: Number Representation of a Biased Coin
There are generally two steps in writing a program to simulate events. The first step is to build a model
of the possibilities by dividing the interval [0, 1) into appropriate sized pieces to represent the likelihood
of each event. The second step is to write the program that uses the model built.
Example 8-3. Write a program that simulates ten tosses of a biased coin where 35% of the time a flip is
expected to produce a head and 65% of the time a flip is expected to produce a tail. Output the result
of each flip.
SOLUTION:
Rem Simulate ten tosses of a biased (.47-.53)
Rem coin and displays the results.
Rem OUTPUT: Text with the results of the toss
Randomize
Cls
For I = 1 To 10
A flip = Rnd
Print “Flip “ I “: “;
If flip 0.35 Then
Print “The coin came up heads.”
Else
Print “The coin came up tails.”
End If
Next I

149
Random Numbers
OUTPUT:
COMMENTS: The Rnd function at A generates a number between 0 and 1 (excluding 1) and assigns
that number to flip. If the number produced is less than 0.35, the coin is said to come up heads. If the
number produced is greater than or equal to 0.35, the coin is said to come up tails. We can use this kind
of reasoning with the Rnd function to simulate any situation in which we know the probability of the
occurrence of each possible event (in this case, two events-heads and tails). Observe that the probability
of all the events should add up to 1.
On Your Own
1. Liam has a batting average of .292. Write a program that simulates Liam’s at bats in baseball
games during which he bats 100 times. Display the total number of hits made by Liam. A
batting average of .292 means that 29.2% of all the times at bat the batter got a hit. (Sacrifice
flies, bunts and walks are not counted in the total number of at bats.)

150
Random Numbers
8.5 Die Rolling
In the last section, we represented the occurrences of events with numbers ranging between 0 and 1
that are generated by Rnd. We can use this method to simulate the roll of a die. A regular die has six
sides to produce a total of six possible equally likely outcomes: 1, 2, 3, 4, 5, 6. Each outcome has a 1/6
chance of occurring. For this situation, we must break up the numbers between 0 and 1 into six equally
sized groups. Thus, we will place divides at 1/6, 2/6, 3/6, 4/6, 5/6 and 1 in the model of this process. We
then assign to each of these intervals the event that each value in the interval is taken to represent. For
example, all the random numbers between 0 and 1/6 could represent rolling a die and having 1 on the
top face when the die comes to rest. See Figure 8-5 for one possible model for rolling a die. (There are
6 * 5 * 4 * 3 * 2 * 1 possible ways to assign outcomes to the six equal sized subintervals.)
Top
Face 1
Top
Face 2
Top
Face 3
Top
Face 4
Top
Face 5
Top
Face 6
0 1/6 1/3 1/2 2/3 5/6 1
Figure 8‑5: Number Representation of the Results of a Roll of a Die
When a random number is in [0, 1/6) we will say a 1 has been rolled. When a random number is in
[1/6, 2/6) we will say that a 2 has been rolled. This pattern continues up to the resulting roll of six when
the random number is in [5/6, 1).
The assignment of events to intervals can be done in many different ways when all the events are equally
likely because any interval can represent any one of the events. For example, Figure 8-6 gives another
model for rolling a die.
Top
Face 1
Top
Face 5
Top
Face 3
Top
Face 2
Top
Face 6
Top
Face 4
0 1/6 1/3 1/2 2/3 5/6 1
Figure 8‑6: Number Representation of the Results of a Roll of a Die
When different events have different likelihood of occurring, the interval that represents a particular
event can be placed anywhere in the interval [0, 1) or even be a collection of disjoint intervals as long
as the length of the interval or intervals assigned to a particular event is equal to the probability of the
event happening. Any event must be represented by subintervals of [0, 1) that are disjoint from the
subinterval(s) representing any other event.
Example 8-4. Write a program that simulates ten rolls of a die. The program should print the result of
each roll.

151
Random Numbers
Model: Top
Face 1
Top
Face 5
Top
Face 3
Top
Face 2
Top
Face 6
Top
Face 4
0 1/6 1/3 1/2 2/3 5/6 1
SOLUTION:
Rem Simulate ten rolls of a die and display the results
Rem OUTPUT: Text with the results of the rolls
Randomize
Cls
A For I = 1 To 10
Rem Get a random number
B x = Rnd
Rem See what value represents the random number
C If x 1 / 6 Then
roll = 1
ElseIf x 2 / 6 Then
roll = 2
ElseIf x 3 / 6 Then
roll = 3
ElseIf x 4 / 6 Then
roll = 4
ElseIf x 5 / 6 Then
roll = 5
Else
roll = 6
End If
Rem Print the value on the top face of the die
D Print “Roll “ I “: The top face ended up as “ roll “.”
E Next I

152
Random Numbers
SAMPLE OUTPUT:
Roll 1: The top face ended up as 3.
COMMENTS: The For .. Next loop beginning in A and ending with E causes its body to be repeated
ten times to simulate ten rolls of the die. In B the Rnd function generates a random number between
0 and 1. Beginning in C, the If block associates the random number with an event. Each case of the If
block identifies one of the six possible results of rolling a die. Once the result of the roll is determined,
the program transfers control to D where the result is printed. The condition could also be coded as six
If .. Then .. End If statements, the first two of the form:
give us a call on +44 (0)20 7000 7573.
The next step for
top-performing
graduates

153
Random Numbers
If (x 1/6) Then
roll = 1
End If
If (x = 1/6) And (x 1/3) Then
roll = 2
End If
Remember the mathematical notation 1/6 = x = 1/3 is not valid in BASIC. Also, in an If .. ElseIf
statement as soon as a condition is found to be true some action is taken and control passes to the first
statement following EndIf. In the Print statement the string concatenate operation makes the output
look better-try a semicolon to see the difference.
8.6 Scaling the Rnd Function
The program in Example 8-4 correctly simulates the roll of a die but it is a bit difficult to understand.
The program would be more convenient and easier to follow if we could produce random numbers in
ranges other than 0 and 1. There are several ways in which we can scale the Rnd function so that it
produces random numbers with different ranges. For example, if we multiply the Rnd function by a
number N, the range of numbers produced will be stretched to represent the interval [0, N). Specifically,
the following statement
stretchedNum = 6 * Rnd
assigns to stretchedNum a random number between 0 and 6 (since multiplying a number in [0, 1) by 6
will result in a number in [0, 6)). The previous command would produce numbers such as those shown
in Table 8-1 using the random numbers shown.
Rnd 6 * Rnd
0.3482477 2.089486
0.7303234 4.381941
0.0138204 0.082922
0.3116572 1.869943
0.8606638 5.163983
Table 8‑1: Random Numbers Scaled by 6
If we prefer to deal with integer numbers rather than with decimal numbers, we can use the Int()
function to remove the digits to the right of the decimal point. The Int() function truncates a decimal
number or “throws away” the digits to the right of the decimal point. See Table 8-2 for examples of the
Int() function applied to the numbers in the second column of Table 8-1.

154
Random Numbers
Operation Result
Int(2.089486) 2
Int(4.381941) 4
Int(0.082922) 0
Int(1.869943) 1
Int(5.163983) 5
Table 8‑2: Example Results of the Int() Function
Thus, if we apply the Int() function to the values of Rnd that are scaled by some factor N, we can produce
random integers within the range 0, 1, …, N-1. For example, the following statement
die = Int(6 * Rnd)
Get Started
Get a higher mark
on your course
assignment!

155
Random Numbers
assigns to die one of the following integer values: 0, 1, 2, 3, 4 or 5. Now say that we want to generate
integers that simulate the roll of a die. We want to generate random integers between 1 and 6 inclusive
and not 0 to 5. To do this, we can simply add one to the range of numbers we just produced. For example,
the following statement
die = Int(6 * Rnd) + 1
assigns to die one of the following integer values: 1, 2, 3, 4, 5 or 6. See Table 8-3 for examples of this
addition operation applied to the numbers in the second column of Table 8-2.
Operation Result
Int(2.089486) + 1 3
Int(4.381941) + 1 5
Int(0.082922) + 1 1
Int(1.869943) + 1 2
Int(5.163983) + 1 6
Table 8-3: Example Results of Int(6 * Rnd) + 1
Thus, the above statement simulates the roll of a die and assigns the value of the roll to die. This scaling
technique works when all the events are equally likely. Notice that we do not need a sequence of if
statements to determine the interval that contains the random number so the program is much simpler
as shown in Example 8-5.
Example 8-5. Use the scaling process on the output of the Rnd function to write a program that simulates
ten successive rolls of a die and displays the results.
SOLUTION:
Rem Simulate ten rolls of a die and
Rem display the results.
Rem OUTPUT: The results of repeated rolls of a die
Randomize
Cls
Print “Output of 10 rolls of a die.”
For I = 1 To 10
roll = Int(6 * Rnd) + 1
A Print roll;
Next I
B Print

156
Random Numbers
COMMENT: The print statement in B causes the printer to advance to the beginning of the next line as
all the random numbers generated and printed in A appear on a single line. (Can you tell why?)
The game of craps involves computing the sum of the number of spots on the top faces of two die. This
is actually one of the “fairest” casino games. You win if you subsequently roll two die that have the same
sum for the values on their top faces. You lose when the sum of the top faces is seven except rolling
seven with your first roll is an automatic win.
Example 8-6. Modify the program from Example 8-5 to roll a pair of dice ten times and calculate the
sum of the spots on the top faces of the two die when they come to rest.
OUTPUT: 6 9 5 9 7 12 6 11 8 7
SOLUTION:
Rem Simulate ten rolls of a pair of dice and displays
Rem the results (sum of spots on top faces).
Rem OUTPUT: Sum of the spots on the top faces of two die
Randomize
Cls
Print “The sum of the top faces of two die rolled 10 times.”
For I = 1 To 10
A die1 = Int(6 * Rnd) + 1
B die2 = Int(6 * Rnd) + 1
C roll = die1 + die2
Print roll;
Next I
Print
COMMENTS: In the program there is no need for a large If block to associate the random number with
a result of a roll. The statements in A and B generate integers in the range 1 to 6. Thus, each statement
directly simulates the result of rolling one die. To find the results of the roll of the pair of dice, the two
separate results are added in C.
Example 8-7. Write a program that simulates a lottery drawing in which four ping pong balls are selected
from four separate bowls each containing 10 ping pong balls. Each ball is marked with an integer from
0 to 9. (This program is similar to the die rolling program except that the random numbers generated
are in a different range.)
MODEL: The value in the interval represents the event represented by every number in the interval.

157
Random Numbers

SAMPLE OUTPUT:
The winning lottery number for Saturday is:
6 0 7 3
SOLUTION:
Rem Simulate a lottery drawing in which four random
Rem numbers R1, R2, R3, and R4 from 0 to 9 are used to generate
Rem the four digit number R1 R2 R3 R4.
Rem OUTPUT: Text with the winning number
Randomize
Cls
Print “The winning lottery number for Saturday is:”;
Print
A For I = 1 To 4
B num = Int(10 * Rnd)
C Print Format(num, “@@”);
Next I
D Print
COMMENTS: The For .. Next loop beginning in A repeats four times to produce the four digits needed
to determine a winner of the lottery. The expression in B, Int(10 * Rnd), first generates a random integer
in [0, 1) and then scales the value to be in [0, 10). The Int function produces one of the integers 0, 1, 2,
… , 8, and 9. The semicolons in the print statement (C) cause the four digits to be printed on the same
line close together with the first number the coefficient of 1000, the second number drawn is interpreted
as the coefficient of 100, the third number drawn is interpreted as the coefficient of 10, and the final digit
drawn is interpreted as the ones digit of the winning number. The print statement (D) causes the printer
to advance to the next line. The Format() command is used to give a consistent spacing to the answer.
On Your Own
1. Write a program that simulates rolling a twelve-sided die (with the numbers 1 through 12 on
the sides). Each side is equally likely to occur. Roll the die 15 times and display the results of
the rolls.

158
Random Numbers
2) Write a program that simulates dealing three five card hands from the standard deck of 52
cards (don’t worry about how the cards are named). Run the program 50 times and see if
the first card is ever dealt again.
3) Write a program that totals the amounts N customers spend if the amount spent by each
customer is a randomly generated number between 0 and $12.00. Use 12 *Rnd to compute
how much a customer spends.
8.7 A Simulation
If we know the probability of the occurrence of all possible events in some game or scenario, we can often
use random numbers to simulate these games. For instance, we saw how to simulate flipping a coin. We
can use similar methods to simulate situations in which more than two events may occur.
Example 8-8. Write a program that simulates the sales of 20 cars sold by a used car dealership in a
typical month. Each time a car is sold, there is a 50% chance that the car will be a Ford, there is a 35%
chance that the car will be a Toyota, and a 15% chance that the car will be a BMW. (See Table 8-4.) These
percentages were determined by examining all sales records of a large dealership for a two year period.
The program should print the name of the car make for each car sold and how many of each car make
were sold in a typical month.
Car Make Percentage of Sales
Ford 50%
Toyota 35%
BMW 15%
Table 8-4: Car Makes and Percentage of Sales
To simulate the sales by this dealership, we must first construct a model showing how the numbers in
[0, 1) will represent the sale of different kinds of cars. We divide the numbers between 0 and 1 into three
intervals so that each interval represents the sale of a car of a particular make. Since the probability of
each car being sold is different, the sizes of the intervals reflect this. We refer to each car’s percentage of
sales in order to make the proper divisions of the numbers between 0 and 1. See Figure 8-7 for a model
of this simulation.
Ford Toyota BMW
0 0.5 0.85 1
Figure 8-7: Number Representation of the Percentage Sales of Each Car Make

159
Random Numbers
When a random number is in [0, 0.5), we say that a Ford has been sold. When a random number is in
[0.5, 0.85), we say that a Toyota has been sold. When a random number is in [0.85, 1), we say that a
BMW has been sold.
OUTPUT:
Out of 20 sales, the following
number of each make was sold.
Ford 11
Toyota 7
BMW 2

160
Random Numbers
SOLUTION:
Rem Simulate twenty car sales and display how many of each
Rem car make were sold using a model based on previous sales:
Rem 50% Ford, 35% Toyota, 15% BMW.
Rem OUTPUT: How many cars of each model were sold
Randomize
Cls
Rem Initialize sales of each make
A ford = 0
toyota = 0
bmw = 0
Rem Simulate 20 sales
B For I = 1 To 20
C x = Rnd
D If x 0.5 Then
ford = ford + 1
ElseIf x 0.85 Then
toyota = toyota + 1
Else
bmw = bmw + 1
End If
E Next I
Rem Display output
F Print “Out of 20 sales, the following”
Print “number of each make was sold.”
Print
Print “Ford”, ford
Print “Toyota”, toyota
Print “BMW”, bmw
COMMENTS: Beginning in A the number of sales of each car make is initialized to zero. In C, the
Rnd function generates a number between 0 and 1. Beginning in D, the If block associates the random
number with a corresponding car make. When the interval for a random number is identified and the
program increments the sales count for that make, the program continues at E. At E the increment,
testing, and transfer are carried out until the body of the loop has been executed 20 times. Each case of
the If block increments the number of sales of one of the car brands. The For .. Next loop (B through
E) repeats twenty times to simulate twenty car sales. Finally, beginning in F outside the For .. Next loop,
the results of the sales are displayed.

161
Random Numbers
On Your Own
1. A computer store sells approximately 50 computers per week. A store clerk has estimated
that each time a computer is sold, there is a 55% chance that the computer is an IBM, a
35% chance that the computer is a Macintosh and a 10% chance that the computer is a Sun.
Write a program that simulates one week of sales at the store. Your program should display
how many of each kind of computer was sold.
2. Redo Example 8-8 by first scaling [0, 1) to 1, 2, … , 20 and using the values 1, 2, … , 10
to represent selling a Ford; 11, 12, … , 17 to represent selling a Toyota; and 18, 19, 20 to
represent selling a BMW.
3. Redo Example 8-8 by first scaling [0, 1) to 1, 2, … , 100 and using the values 1, 2, … , 50 to
represent selling a Ford; 51, 52, … , 85 to represent selling a Toyota; and 86, 87, … , 100 to
represent selling a BMW.
1. Smith has a .189 batting average, Jones has a .273 batting average, and Lewis has a .324
batting average. Write a program that simulates 27 at bats in which each player bats nine
times in the order Smith, Jones, and Lewis. Observe that there are three models to use.
Display the total number of hits by each player.
2. Write a program that simulates a dice rolling game. Roll a pair of dice ten times. If a 7 or
an 11 is rolled, record a win. Your program should display the results of each roll and the
total number of wins.
3. Suppose the color of a car is determined by the value of a random number. If a random
number has a value of less than 0.5 color the car red. If the random number is between 0.5
and 0.75 color the car green. Otherwise, color the car blue. If the production line produces
25 cars a day, write a program that simulates choosing the colors of the cars produced on a
typical day. Output the number of cars of each color.
4. Imagine a slot machine that has three equally likely outcomes: orange, lemon and bell.
Write a program that simulates 10 plays.
(a) Output the number of times the outcome was a bell.
(b) Modify (a) so that each play of the game generates two outputs: orange-bell, bell-bell,
lemon-bell, etc. Output the two symbols and indicate whether the two symbols match.
(c) Modify (b) so that each play of the game generates three outputs. Output the three
symbols and indicate whether or not all three symbols match.
(d) Modify (c) so that the program adds 5 to a bankroll when the output is three oranges, 10
when the output is three lemons, and 25 when the output is three bells. Subtract 1 from the
accumulator whenever the three symbols do not match. Start with a bankroll of 25. Output
the value of the bankroll after 100 plays of the game. (Do not output the symbols.)

162
Random Numbers
5. If a player’s at bat in a baseball game takes three minutes 28% of the time, five minutes
40% of the time, and eight minutes the other times, simulate a game with 54 at bats and
determine how long a game may take. Repeat the experiment 50 times and find the average
game time for the 50 simulated games. Hint: All the code for the play of the game can
be part of the true range of a condition that keeps track of whether 50 games have been
completed. The true range of the condition should also sum the time for each experiment so
the average can be computed when the loop finishes.
6. Simulate a slot machine with four outcomes. Two outcomes occur 25% of the time each,
one occurs 35% of the time, and the fourth occurs 15% of the time. The outcomes that
occur 25% of the time have a payoff of $3. The outcome that occurs 35% of the time has a
payoff of $1. The option that occurs 15% of the time has a payoff of $5. If each play costs
$2, compute the winnings for 20 plays of the slot machine. Add an option that will find the
average winnings for any number of 20 plays.
7. For twenty customers simulate their shopping experiences. Suppose there are four different
stores and the sale for each customer at a store is less than $20.00. Use two random numbers,
one to simulate which store the customer visits assuming each store is equally likely to be
chosen. The second random number indicates how much the customer spent at the store they
visited. Compute how many customers went to each store and the total sales for each store.
8. Repeat problem (7) but now assume the purchase by a customer was in the range:
$5.00 purchase amount $25.00.

163
Graphics
9 Graphics
Graphs and charts can show relationships that exist between and among data elements. Animations can
be used to create films or commercials by putting together a sequence of graphical images. All these
graphical objects are applications of computer graphics. This chapter gives an insight into how computer
graphics are created using BASIC programming.
Spreadsheets make graphical display of data very easy. Underlying the ease spreadsheets provide for
the user is the kind of programming that is introduced in this chapter. In Figure 9-1 a pie chart gives
a visual representation of three categories of expenses and shows how the relative size of each class of
expenses took up part of all expenses.
'UDZDFLUFOH
3RVLWLRQLQJ
WH[WDQG
FRPSXWLQJ
SHUFHQWV
'UDZLQJVHFWRUV
LQWKHFLUFOH
Figure 9‑1: Pie Chart
9.1 Resolution and Color
Personal computers and laptops have color monitors and full color graphics display capabilities. The
output form defined in the template code creates a graphics display area divided into 425 rows of 720
columns each. This form is organized as 306,000 pixels, small points on the screen that can be individually
accessed and colored.
To create graphics on a screen, we use commands that refer to particular pixels on the screen. Each pixel
has an address on the screen. The pixels are numbered using two coordinates, the first increasing as you
move from the left margin of the form to the right (column numbers). The second coordinate increases
as you move from the top of the form towards the bottom of the form (row numbers) on the screen. A
pixel’s address consists of its column number and its row number. Figure 9-2 shows the addresses of the
pixels at the corners of the display area.

164
Graphics
(0, 0) (719, 0)
(0, 424) (719, 424)
Figure 9‑2: Addresses of Corner Pixels
Graphic images are produced by changing the colors of pixels. Each pixel can be separately assigned a
color. BASIC has a number of predefined color constants that may be used that are listed in Table 9-1.
Color Constant Color
vbBlack Black
vbBlue Blue
vbGreen Green
vbRed Red
vbCyan Cyan
vbMagenta Magenta
vbYellow Yellow
vbWhite White
Table 9‑1: BASIC Color Constants
A color is composed of three components: red, green, and blue. The RGB() function built into BASIC
may be used to specify a color in BASIC. The RGB() function takes three arguments. Each argument is
a value between 0 and 255 indicating the strength of the component’s color. The first argument specifies
the red component (R), the second specifies the green component (G), and the third specifies the blue
component (B). See Table 9-2 for a list of standard colors and their RGB() specifications. Note, for
example, that yellow is produced by setting the red and green components to the maximum value and
setting the blue component to the minimum value.
Color RGB specification
Black RGB(0, 0, 0)
Blue RGB(0, 0, 255)
Green RGB(0, 255, 0)
Red RGB(255, 0, 0)
Cyan RGB(0, 255, 255)
Magenta RGB(255, 0, 255)
Yellow RGB(255, 255, 0)
White RGB(255, 255, 255)
Table 9‑2: Standard Colors and their RGB Specifications

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Graphics
The RGB() function may be used whenever a color can be specified. For example, to change the default
background color of the display, the built-in BackColor variable is assigned a different color. To change
the background color to blue, use the command:
BackColor = RGB(0, 0, 255)
There is a similar variable ForeColor that can be assigned a vb-color or an RGB setting to indicate the
color used to draw on the background color.
9.2 Coloring Pixels
Graphics in BASIC can be thought of as drawing pictures on the screen. Drawing pictures is the result of
coloring pixels one at a time until the final picture appears because some set of pixels have been assigned a
different color from the background color. The screen starts out with every pixel colored in the BackColor.
PSet() is the BASIC command to color pixels The PSet() command takes two parameters: a pixel address
and a color. The first parameter, (a, b), is the location of the pixel to be colored. Remember (a,b) uses a to
measurethedistancefromtheleftsideofthe screenandb tomeasurethedistancefromthetopof thescreen.
The second parameter, color, is the color that the pixel will be colored. However, if the color parameter
is omitted from PSet(), the pixel will be colored with the current value of ForeColor. BASIC starts with
default values for both BackColor and ForeColor. Table 9-3 shows examples of valid PSet() commands.
360°
thinking.
Dis
Deloitte Touche LLP and affiliated entities.
360°
thinking.
360°
thinking.

166
Graphics
PSet command Result
PSet (90, 210) Color pixel (90, 210) the foreground color
PSet (9, 11), vbYellow Color pixel (9, 11) yellow
PSet (409, 102), RGB(98, 22, 144) Color pixel (409, 102) purple
Table 9‑3: Example PSet Commands
SYNTAX
Pset(*,*),color
PSet(over, down) changes the color of the pixel at (over, down) from the
background color to the value of color. If no explicit value for color is used, the
pixel is colored with ForeColor.
On Your Own
1. Explain why the following PSet statements are invalid.
PSet 89, 10
PSet (90, 12) vbRed
PSet (54, 39); RGB(33, 202, 188)
Example 9‑1. Using the PSet() command, write a program that colors the pixels (100, 100), (100, 101),
(100,102), … , (100, 300) in the foreground color. The program should then color the pixels (350, 100),
(350, 101), (350, 102), … , (350, 300) with the background color. Finally, the pixels (550, 100), (550,
101), (550, 102), … , (550, 300) should be colored with cyan. Notice that the second line is “invisible.”
OUTPUT:

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Graphics
The pixels that are arguments for PSet() change color. The machine is usually so fast that you cannot
actually see the lines drawn pixel by pixel with the different colors.
SOLUTION:
Rem Colors a series of pixels on the screen
Rem in the foreground color. Then
Rem colors a series of pixels in the
Rem background color. Finally, it colors a series
Rem of pixels with vbCyan.
Rem OUTPUT: Points on the screen in three colors
Cls
Rem Draw the points in the foreground color
A For down = 100 To 300
B PSet (100, down)
C Next down
Rem Draw the points in the background color
D For down = 100 To 300
E PSet (350, down), BackColor
F Next down
Rem Draw the points in cyan
G For down = 100 To 300
H PSet (550, down), vbCyan
I Next down
COMMENTS: The commands at A, B, and C draw the points (100, 100) to (100, 300) in the foreground
color. The For .. Next counter variable, down, represents the numbers 100 to 300 and is used in the pixel
address in B. The For .. Next loop beginning in D is the same as that beginning in A, except that the
points are drawn in the background color at a location 350 pixels from the left edge of the window. Finally,
the For .. Next loop beginning in G once again draws a line, but this time the pixels are drawn in cyan.
To cause the program to pause, we can use the InputBox() function to ask the user to press the Enter key:
pause = InputBox(“Press Enter to continue.”)
The effect of this command is to freeze the screen as it is until the user presses the Enter key. When the
user presses the Enter key, the program will continue. If you include this command after C and F, you
will see the lines drawn one at a time.
Example 9‑2. Modify the previous example program to pause each time a line is completed.

168
Graphics
SOLUTION:
Rem Colors a series of pixels on the screen in the foreground color.
Rem Then colors a series of pixels in the background color.
Rem Finally, it colors a series of pixels cyan.
Rem OUTPUT: Points on the screen in three colors
Cls
Rem Draw the points in the foreground color (black)
For down = 100 To 300
PSet (100, down)
Next down
Rem Pause for user
A pause = InputBox(“Press Enter to continue.”)
Rem Draw the points in the background color (white)
PSet (350, down), BackColor
Next down
Rem Pause for user
B pause = InputBox(“Press Enter to continue.”)
Rem Draw the points in cyan
PSet (550, down), vbCyan
Next down
COMMENTS: In the solution program, the commands in A and B cause the program to pause so that
the user can see the results of the For .. Next code above it. An execution of this program would clearly
show the points along the line first in black and the third line in cyan. The second line was drawn in
the background color so you do not “see” it.
A For .. Next command is a natural way to go about changing the color of the pixels in these two
programs. The resulting figures were just vertical lines but the idea of how to draw any line should be
intuitively clear. We must change the color of all the pixels on the line segment from one end point of
the line to the other endpoint of the line segment. The problem is to figure out the addresses of just
those pixels that lie on the line to be drawn.
On Your Own
1. Write a program that sets the screen background color to green. Draw the line segment with
endpoints (0, 75) and (200, 75). The line segment should first appear in the color white and
then, after a pause, change to the color blue.
2. Using the program in Example 9-2 as a model incorporate the STEP option with an
increment of 3 to see how dashed lines can be drawn.

169
Graphics
9.3 Drawing Lines
With the ability to draw lines comes the ability to create boxes, charts, graphs, parallelograms, and
polygons of any size. The ideas we explore learning to draw lines with BASIC shows us how circles and
any figure that can be described by a function can be drawn.
Drawing a line starts with the identification of the two endpoints of the line segment. Suppose we want
to draw the line from the point (100, 75) on the output form to the point (250, 315). These two points
are shown in Figure 9-3.
Figure 9‑3: Two Points on the Output Form

170
Graphics
In Figure 9-4 we see a dashed line joining (100, 75) to (250, 315). What we need to determine is the
location of each pixel along the dashed line so we can color them differently from the background color.
Figure 9-4: Dashed Line joining the Endpoints
The obvious answer is to find the equation of the line joining (100, 75) to (250, 315).
The fundamental property about lines is that the slope can be computed using any two points on the line
and in fact no matter which two points are used, the value of the slope is always the same. The slope of
a line joining two points (over1, down1) and (over2, down2) is simply
GRZQGRZQ
RYHURYHU
If we let (over1, down1) = (100, 75) and (over2, down2) = (250, 315), the slope of the line joining them is

The next step in finding the equation of this line is to compute the slope again using one of the given
points and an arbitrary point on the line (see Figure 9-5). Let us choose the point (over, down) as
an arbitrary point on the line. Now when we compute the slope for the two points (over1, down1) =
(250, 315) and (over2, down2) = (over, down) we get:
GRZQ
RYHU

171
Graphics
Figure 9‑5: Three Points on the Line
We can now use the property of a line that says the slope is the same regardless of which two points on
the line are used to compute it to set our two computations equal to each other:
GRZQ

RYHU
Figure 9-6 summarizes the steps we must take to complete finding the equation of the line with endpoints
(over1, down1) = (100, 75) and (over2, down2) = (250, 315) and an arbitrary third point on the line
denoted as (over, down).
Step 1: Write the formula
GRZQGRZQ

GRZQGRZQ
RYHURYHU RYHURYHU
Step 2: Substitute the known values
GRZQ

RYHU
Step 3: Clear the left fraction of its denominator
down - 315 = (315 - 75)/(250 - 100) * (over - 250)
Step 4: Make the left side contain only the variable
down = (315 - 75)/(250 - 100) * (over - 250) + 315
Figure 9‑6: Finding the Equation of the Line with Endpoints (100, 75) and (250, 315)

172
Graphics
On Your Own
1. Find the equation of the line with endpoints (50, 100) and (125, 200). First represent the
down coordinate as a function of the over coordinate.
2. Find the equation of the line with endpoints (50, 100) and (125, 200). First represent the
over coordinate as a function of the down coordinate.
9.4 Using the PSet Command
To draw the line once the equation of the line is known involves changing the color of all the pixels
with over coordinate:
over1, over1 + 1, over1 + 2 , … , over2 – 2, over2 – 1, over2
where we assume over1 over2. For the moment we will avoid dealing with the down coordinate of
these points and just set up the code so that all these over values are used. The code is simply a For ..
Next loop as shown in Table 9-4.
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for development
Potential
for exploration

173
Graphics
For over = over1 To over2
….
Next over
Table 9‑4: Code to Visit All the over Values for Drawing a Line
In Figure 9-7 we see the over coordinate at 185 and 210 and how it needs to find the appropriate down
coordinate for each step of its way.
Figure 9‑7: Relationship between over and down in Drawing a Line
The appropriate down is just the value of the equation of the line joining the two points evaluated at the
current value of over. For a particular value of over its down coordinate on the line is just
down = (down2 – down1) / (over2 – over1) * (over – over2) + down2
The code to change the color of the pixel just for the point (over, down) is:
PSet(over, (315 - 75) / (250 - 100) * (over - 250) + 315)
Now to change the color for each pixel on the segment we just put this command into the For .. Next
command that makes over take on all the required values. The code is shown in Table 9-5.
For over = 100 To 250
PSet(over, (315 – 75) / (250 – 100) * (over – 250) + 315)
Next over
Table 9‑5: Drawing a Line

174
Graphics
Another example of drawing a line is given in Example 9-3.
Example 9‑3. Write a program that draws in blue the line segment with endpoints (75, 75) and (250,
375). Use the equation of the line:
down = (375 - 75) / (250 - 75) * (over - 250) + 375
where over ranges from 75 to 250.
OUTPUT:
SOLUTION:
Rem Draw the line with endpoints (75, 75) and (250, 375)
Rem OUTPUT: The specified line segment
Cls
Rem Draw the line in blue
A For over = 75 To 250
B down = (375 - 75) / (250 - 75) * (over - 250) + 375
C PSet (over, down), vbBlue
Next over
COMMENTS: The For..Next loop beginning in A references each point with an over coordinate between
75 and 250. The assignment statement in B uses the equation of the line to calculate the corresponding
value of down. The PSet() statement in C colors pixels in blue.
What we have really seen is that for any figure that can be described by an equation, we can draw the
output of the function one pixel at a time. Unfortunately, most functions are not as easy to manipulate
algebraically as a line. The principles are the same, however.

175
Graphics
On Your Own
1. Write a program that draws a green line with endpoints (50, 100) and (125, 200).
2. Write a program that draws a line joining the points (55, 255) and (150, 320).
9.5 Using the Line Command
The line is a fundamental form that can be used to draw more complex figures, such as triangles and
rectangles. The fact that a line can be part of so many figures would make it nice to have all the code
encapsulated into a single BASIC command. We have seen effective encapsulation in the For .. Next
command and something similar for drawing a line would be helpful. BASIC does, in fact, include a
command to draw a line given only the two end points. The SYNTAX for this is:
Worldwide (2014)
APPLY HERE

176
Graphics
SYNTAX
Line
Line (a1, b1) – (a2, b2), color
(a1, b1) and (a2, b2) are the starting and ending points of the line to be drawn. If (a1, b1)
is missing, the line drawn starts at the pixel last accessed by the program but a hyphen
must be included before (a2, b2).
color specifies the color in which the line is drawn. If color is not specified, the default
foreground color is used.
Using the Line command saves us the trouble of computing the equation of the line we wish to draw. Table
9-6 shows the two different ways to draw the line (line segment) with endpoints (50, 25) and (80, 75).
Using PSet Using Line
For over = 50 To 80 Line (50, 25)-(80, 75)
down = (75 - 25) / (80 - 50)*(over - 80) + 75
PSet (over, down)
Next over
Table 9‑6: Two Ways to Draw the Line with Endpoints (50, 25) and (80, 75)
In Table 9-6 the first way to draw the line is to use a PSet() command. The second way is to use the
Line command. In the second way, the single Line command replaces the four lines which make up the
For .. Next loop in the first way. It is obvious that using the Line command is much more convenient
and intuitive. BASIC graphics commands are ways of allowing the programmer to think at a higher level
instead of at the level of individual pixels.
We show the two lines:
a) Line (65,40) - (200, 30)
b) Line (150, 100) - (375, 230), RGB(200, 100, 100)
drawn with the Line command in Figure 9-8.

177
Graphics
/LQH ±
/LQH ± 5*%
Figure 9‑8: Drawing of Two Lines
9.6 Drawing Rectangles
Once we understand how lines are drawn by BASIC, we can ask if there are additional figures, such as
rectangles, that can be as easily drawn. In Figure 9-9 we show the line joining (250, 140) and (375, 270).
Figure 9‑9: A Line and Its Endpoints
If the two endpoints in Figure 9-9 were opposite corners of a rectangle and not the endpoints of a line
segment,wewouldneedtofindthecoordinatesoftheothertwocornerstoknowhowtodrawtherectangle
with these four corners. What we need to do is identify the corners labeled B and C in Figure 9-10.

178
Graphics

$
%

'

Figure 9‑10: Corners of a Rectangle
We see that C is over the same amount as A so its over coordinate is 250. C is down the same amount
as D so its down coordinate is 270. B is over the same amount as D so its over coordinate is 375, Finally,
B is down the same amount as A so its down coordinate is 140. Now that we know the coordinates of
these four points, we must get BASIC to draw the four lines that form the rectangle with these four
points as corners. We draw
Line (250, 140) – (375, 140)
Line – (375, 270)
Line – (250, 270)
Line – (250, 140)

179
Graphics
but not the line from (250, 140) to (375, 270). This is exactly what BASIC will do if we use an additional
option in the line command.
SYNTAX
Line / Box Command
Line (a1, b1) - (a2, b2), color, B or BF
(a1, b1) and (a2, b2) are the starting and ending points on the display of the line to be
drawn.
color specifies the color in which the line is drawn. If color is not specified, the default
foreground color is used.
If B is specified, a box is drawn with (a1, b1) and (a2, b2) as opposite corners. BF produces
a box filled in with the specified color or the default color if no color argument is used.
You may use B without F but you may not use F without B.
On Your Own
1. Explain why the following Line statements are invalid.
a) Line
b) Line (67, 89), vbBlue
c) Line (78, 100)-(100, 99) B
d) Line (24, 5)-(75, 150), vbYellow, F
2) What does the command Line –(200,200) mean?
Example 9‑4. Using the variations of the Line command, write a program that draws two lines, one
from (20, 100) to (200, 100) and the other from (200, 100) to (20, 10) in cyan. Also draw a box with
corner points (270, 75) and (450, 200) and a filled box with corner points (550, 375) and (675, 150)
having color green.

180
Graphics
OUTPUT:

/LQH ±
/LQH±
/LQH ± %
/LQH ± YE*UHHQ%)
SOLUTION:
Rem Draw two lines, a box
Rem and a filled box.
Rem Output: 2 lines, a box and a filled box colored green
Cls
Rem Draw a line using the foreground color
A Line (20, 100) - (200, 100)
Rem Draw a line in the color cyan
B Line - (20, 10), vbCyan
Rem Draw a box using the foreground color
C Line (270, 75) - (450, 200), , B
Rem Draw a filled box in the color green
D Line (550, 375) - (675, 150), vbGreen, BF
COMMENTS: In the solution program, the Line statement in A draws a line from (20, 100) to (200,
100) in the default foreground color. B draws a line from the last referenced point, (200, 100), to (20,
10) in the color cyan. C draws the boundary edges of a box with (270, 75) and (350, 200) as opposite
corners using the foreground color. D draws and fills-in with the color green a box with (550, 375) and
(675, 150) as opposite corners.
Unfortunately, the Line command can only draw rectangles automatically but not parallelograms or
trapezoids. Other four sided figures have to be drawn using the Line command four times.
Example 9‑5. Use the Line command to draw the polygon shown below.

181
Graphics
OUTPUT:
your chance
to change
the world
• IMS and IPTV

182
Graphics
SOLUTION:
Line (82, 50) - (275, 40)
Line - (220, 103)
Line - (70, 110)
Line - (82, 50)
On Your Own
1. Write a program that draws a picture of a house. Your house should look like the figure
below:
Notice that all the features are lines and boxes (the door is a box, the window frames are boxes, and a
portion of the house without the roof is a box).
9.7 Drawing Circles
NowthatwehaveseenhowBASICencapsulatesdrawinglinesintoasinglecommandthatcanbeextended
to draw rectangles, we want to explore one other BASIC figure that is drawn with a single command. The
figure is the circle. Since a circle can be drawn if we know its center and its radius, it is not surprising
that BASIC’s circle command asks for these two values. The syntax is described next.
The following are examples of valid Circle commands that draw the circles in Figure 9-11.
Circle (150, 200), 75
Circle (400, 200), 75, vbRed
Circle (400, 300), 75

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Figure 9‑11: Three Circles
Filling in a circle with a color will be explained when we discuss FillStyle and FillColor.
On Your Own
1. Explain why the following Circle statements are invalid.
Circle (90, 45)
Circle (10, 100); 5
Circle , 50, vbCyan
2. Write a program that draws a circle centered at (100, 75) with radius 30 pixels. Any color
can be used for the boundary.
SYNTAX
Circle
Circle (over, down), rad, color
(over, down) is the pixel location of the center of the
circle. rad is the radius of the circle and color indicates
the color to be used to draw the circle boundary.

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9.8 Drawing Arcs
Suppose there is a circle with center (a, b) and radius rad. The circumference of the circle, which
measures the length of the boundary of the circle, is 2π rad. To draw an arc of the circle we need to
identify the starting and ending points along the boundary of the circle. We do this by indicating how
far around the circle from (a+rad, b), we traverse to get to the starting point of the arc. We then indicate
how far the ending point is from the same starting point. Thus, if we include in the Circle command
both the starting and ending points of an arc in terms of where these points are located as we traverse
the circumference of the circle, BASIC can draw just that portion of the circle. To draw an arc that
starts at (a+rad, b) we are talking about a starting point with zero distance from this point along the
circumference of the circle. BASIC does not allow 0 as a starting point but requires we use some small
value like 0.01. In Figure 9-12 we see a circle labeled with the measure for 1/4, 1/2, and 3/4 of the way
along the circumference. If we define
pi=3.14159
these points are pi/2, pi, and 3 * pi /2 radians from the starting point.
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Figure 9‑12: Distance Along the Circumference of a Circle
SYNTAX
Circle (Arc)
Circle (over, down), rad, color, start, end
(over, down) is the center of the circle, rad is the radius of the
circle, and color indicates the color to be used to draw the circle.
Start and end indicate the starting and ending points of an arc on
this circle. Start and end are distances along the circle from the
starting point (over +rad, down).
Arcs are always drawn in the counter-clockwise direction. Suppose that we want to draw the semi-circle
that makes up the right half of a full circle. See Figure 9-13.
Figure 9‑13: Semi-circle that Makes up the Right Half of a Full Circle
To draw this semi-circle, we would specify 4.71239 (3π/2) as the start parameter. We would then draw
the arc in the counter-clockwise direction and specify 1.57079 (π/2) as the end parameter. Thus, the
following statement would produce the semi-circle shown in Figure 9-6.

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Graphics
Circle (350, 250), 85, , 4.71239, 1.57079
The arc begins at 3π/2 and continues in the counter-clockwise direction until it reaches π/2. The pair of
consecutive commas indicates the default color is used to draw the arc.
It is very important not to try to draw an arc in the clockwise direction. If you do so, your results will be
very different from what you expect. For instance, suppose we tried to draw the arc in Figure 9-13 in a
clockwise direction. We would have then specified the start parameter as 1.57079 and the end parameter
as 4.71239 as in the following statement.
Circle (350, 250), 85, , 1.57079, 4.71239
Our coordinates would have been backwards, and we would see the results shown in Figure 9-14.
Figure 9‑14: Result of Drawing an Arc with Backwards Parameters
When working with distance along the circumference of a circle, it is useful to create a variable called
pi and use that variable in Circle commands rather than computing distances along the boundary of a
circle directly. If you have the statement
pi = 3.14159
then you can use pi in Circle commands. Assuming the variable pi has been defined, Figure 9-15 shows
the arcs drawn by the following commands:
a) Circle (160, 200), 70, , pi / 2, pi
b) Circle (370, 200), 80, , 7 * pi / 8, pi / 3

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Graphics
Figure 9‑15: Example Arcs
On Your Own
1. Write a program to draw on the screen an arc centered at (200, 75) with radius 50 pixels.
The arc should begin at 0 radians and end at 3π/4 radians. Any color can be used.
Send us your CV on

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Graphics
9.9 Drawing Sectors
A sector is a part of a circle that looks like a piece of pie. A sector has lines that extend from the ends
of an arc to the center of the circle. Figure 9-16 shows a sector of a circle with radius 100 with its center
at (250, 150) and its arc extending from 0 to 3π/2.
Figure 9‑16: An Example Sector
Drawing a sector is easy. It is exactly like drawing an arc with the Circle command except that the start
and end arguments are specified as negative values. Using a minus sign is a convention that BASIC uses
as a signal telling it to draw a sector and not just an arc. Since the start and end points of an arc can
never be negative, using the minus sign allows BASIC to know what to do. To draw the arc of the sector
in Figure 9-16, we would use the statement:
Circle (250, 150), 100, , .01,3* pi /2
(This uses the variable pi defined above.) To draw the sector of this arc, we would simply place negative
signs in front of the start and end parameters as follows:
Circle (250, 150), 100, , -.01,-3*pi / 2
SYNTAX
Circle (Sector)
Circle (over, down), rad, color, -start, -end
(over, down) is the center of the circle, rad is the radius of the circle, and
color indicates the color to be used to draw the circle. Start and end
indicated the starting and ending points of an arc on this circle that will be
drawn. The minus sign on either or both of the start and end arguments
will cause BASIC to draw a line from the center of the circle to the position
on the circle where the arc starts and/or ends.

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Example 9‑6. Use the Circle with center (300,200) and radius equal to 100 to draw a sector that starts
1/5 of the way around the circle and ends 7/8 of the way around the circle.
SOLUTION: Circle (300,200), 100 , ,-2/5*pi, -7/4*pi
On Your Own
1. Write a program to draw a sector with its arc from π radians to 0 radians. The center of the
sector should be at (100, 50), and its radius should be 30 pixels. Any colors may be used.
9.10 Drawing Ellipses
An ellipse is a circle that has been elongated or lengthened or flattened. The last parameter to the circle
command, aspect, is used to specify the ratio of the vertical diameter to the horizontal diameter. If aspect
is equal to 1 then a circle is drawn. The following command
Circle (245,185), 100, , , , 0.5
produces the ellipse shown in Figure 9-17.

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Graphics
Figure 9‑17: An Example Ellipse
SYNTAX
Circle (Aspect)
Circle (over, down), rad, , , , aspect
where aspect is a value between 0 and 1
If aspect is 1, the figure drawn will be a circle. If the aspect is less than 1, a
flattened circle will be drawn.
For aspect equal to 1/2, an ellipse will be drawn. With the aspect equal to 0
a line will be drawn
9.11 Fill Styles
When a rectangle or a circle is drawn, it can be filled with a solid color or a pattern. The built-in variable
FillStyle controls what pattern will be used to fill a figure. Initially FillStyle is set to “transparent,” no
filling is used and anything already inside the figure remains visible. To draw a figure filled with a solid
color, use the command
FillStyle = 0
before drawing the figure. The command FillStyle needs a color to work with. If none is specified,
ForeColor will be used with the particular style chosen. For example, the following commands draw a
circle with a blue border and filled with yellow.
FillStyle = 0
FillColor = vbYellow
Circle (250, 150), 100, vbBlue

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Graphics
The BASIC FillStyle settings are listed in Table 9-7. Up to this point FillStyle has been assigned the
default value of 1.
FillStyle
Setting Description
0 Solid
1 Transparent
2 Horizontal line
3 Vertical line
4 Upward diagonal
5 Downward diagonal
6 Cross
7 Diagonal cross
Table 9‑7: FillStyle Options
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192
Graphics
SYNTAX
FillStyle and FillColor
FillStyle = value : FillColor = color
FillStyle indicates the pattern that will be used to fill in a closed
curve such as a box, a circle, or a sector. FillColor allows user to
choose a color to be used with FillStyle
The program in Figure 9-18 produces three shapes, each with a different FillStyle and a different color.
Rem Draws three filled shapes on the display
Rem OUTPUT: Shapes on the display
Cls
pi = 3.14159
Rem Draw a filled sector
FillStyle = 2 : FillColor = vbGreen
A Circle (120, 100), 100, , -3 * pi / 4, -pi / 4
Rem Draw a sector of an ellipse with a diagonal cross fill
FillStyle = 7 : FillColor = vbCyan
B Circle (350, 60), 100, , -7 * pi / 8, -pi / 8, 1 / 4
Rem Draw a rectangle with a cross fill
FillStyle = 6 : FillColor = vbYellow
C Line (500, 180)-(650, 330), , B
Figure 9‑18: Program that Draws Filled Shapes
The output of the program in Figure 9-18 is seen in Figure 9-19.
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Figure 9‑19: Output of Program in Figure 9-17

193
Graphics
On Your Own
1. Write a program that draws two circles on a blue background. One of the circles should be
outlined in cyan but filled in magenta. The other circle should be both outlined and filled
in green. Use different fill styles for the two circles. The circles may appear anywhere on the
screen.
9.12 A Pie Chart
A common application of graphics with spreadsheet programs is the creation of a pie chart. With the
use of the Circle command and different styles, data can be displayed in pie chart form. The parts of
a pie chart are just sectors of a circle usually filled with different colors and/or styles. An example of a
pie chart appears in Figure 9-20. This pie chart has three sectors, each comprising 33.3% of the chart.
Figure 9‑20: An Example Pie Chart with Three Equal Sectors
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194
Graphics
Example 9‑7. Write a program that creates a pie chart with three sectors. The user enters the size of two
sectors, and the chart is created based on that data.
SOLUTION:
Rem Creates a pie chart with three sectors. The size of
Rem the sectors are based on the user’s data.
Rem INPUT: Percent of circle representing size of each sector
Rem OUTPUT: A pie chart with three sectors
Cls
Rem Get input-integer values for percentages
A sector1 = Val(InputBox(“Enter 1st sector percentage size.”))
sector2 = Val(InputBox(“Enter 2nd sector percentage size.”))
B sector3 = 100 – sector1 – sector2
Rem Initialize variables
C pi = 3.14159
radius = 80
stopangle = .01
Rem Draw each sector
D For I = 1 To 3
E If I = 1 Then
sector = sector1
FillStyle = 3
FillColor = vbBlue
ElseIf I = 2 Then
sector = sector2
FillStyle = 5
FillColor = vbGreen
Else
sector = sector3
FillStyle = 7
End If
Rem Calculate position and size of current sector
F angle = (2 * pi) * sector / 100
G startangle = stopangle
stopangle = startangle + angle
H If stopangle 2 * pi Then
stopangle = .01
End If
Rem Draw the sector
I Circle (160, 100), radius, , -startangle, -stopangle
Next I

195
Graphics
COMMENTS: The program begins by allowing the user to input two sector sizes beginning in A. The
third sector size is calculated (B) based on the first two. Beginning in C, variables that will be used later
are initialized. The For .. Next loop beginning in D draws each sector individually. Within the loop, the
If block beginning in E merely accesses the appropriate sector size to draw. Beginning in F, equations are
used to calculate the size and position of the sector currently being drawn. For instance, in G, a reference
is made to the ending position of the previously drawn sector. In H, the value of stopangle is checked
to ensure that it is not greater than 2π. The Circle command at I actually draws the sector. The radius
of the sector is the value which was initialized in C. FillStyle and FillColor are assigned appropriate
values for each sector in the If block beginning at E.
On Your Own
1. Write a program that creates a pie chart with four sectors. Let three of the sector sizes be
20%, 25%, and 15%. The fourth sector is the remaining portion of the circle. Use different
colors and fill style for each sector.
2. Calculate the starting and stopping points for the sectors of a pie chart where the three
regions represent 50%, 25%, and 25% of the circle.
9.13 Histograms
When values need to be seen in comparison to other values as the sales for a sequence of months or the
number of gyzmos sold each month, the chart called a histogram is effective. A histogram represents
a set of values using a scale so that the relative difference in the magnitudes can be seen by observing
the different heights of a set of rectangles that are proportional to the different values. The output form
shown here displays a histogram for values collected over a period of four months denoted by J(anuary),
F(ebruary), M(arch), and A(pril).
Figure 9‑21: A Histogram
The code to draw the chart in Figure 9-21 is given in Example 9-8.

196
Graphics
Example 9‑8. Draw a histogram representing the four values 120, 200, 90, and 250 that represent sales
in January, February, March, and April, respectively.
Rem: Draw a histogram with four values
Rem INPUT: Four values to be represented
Rem OUTPUT: Histogram representing the relative size of the input numbers
Line (110, 300)-(250, 300)
Line (120, 300)-(140, 300 – 3 * 12), , B
Line (150, 300)-(170, 300 – 3 * 20), , B
Line (180, 300)-(200, 300 – 3 * 9), , B
Line (210, 300)-(230, 300 – 3 * 25), , B
CurrentX = 125: CurrentY = 312
Print “J”
Print “F”
Print “M”
Print “A”
SOLUTION:
In Putting It All Together you will explore ways to make drawing a pie chart or a histogram much more
flexible so that one program can serve a variety of requirement.
1. Write a program that sets background to blue and then draws the points (100, 10) to (100,
100) and (200, 10) to (200, 100). The points should first appear in the color green and then
change to blue and then back to green. There should be pauses between the changes so that
the user can see them occurring.
2. Write a program that draws a picture of a sailboat. Your sailboat may look something like
the figure below:

197
Graphics
3. Write a program that draws a green filled box on the screen. Within that box, draw another
box with a red outline. Fill in the inner box with the color blue.
4. You can add labels to the sectors of a pie chart using code of the following sort when the
circle is centered at (X, Y) and has a radius R.
alpha= (stopangle – startangle) / 2.0
beta = alpha + startangle
If beta pi/2 Then
currentX = X + cos(beta) * R/2
currentY = Y – sin(beta) * R/2
Print “Sector’s label”
ElseIf beta pi Then
currentX = X – cos(beta) * R/2
currentY = Y – sin(beta) * R/2
ElseIf beta pi * 3./2. Then
currentX = X – cos(beta) * R/2
currentY = Y + sin(beta) * R/2
Else
currentX = X + cos(beta) * R/2
currentY = Y + sin(beta) * R/2
End If
Example 9-8 uses three pixels of height to represent one unit in a category. The vertical axis
should be labeled 3, 6, 9, … , 24, 27 units with the label 3 positioned 4*3 pixels about the
horizontal axis.
a) Draw a line from (50,300) to (50,150) to represent the vertical axis.
b) For each of the points 300 – 4*4, 300 – 6*4, … , 200 -27*4 on the vertical axis draw a
tic mark, a line with endpoints (300 – n*4, 50 – 5) and (300 – n*4, 50+5) for n = 1, 2,
… , 10.
c) Use CurrentX and CurrentY to position the print head at
CurrentX = 50 – 5 – 20
CurrentY = 300 – n*4 -8

198
Graphics
where n = 3, 6, 9, … , 24, 27. For CurrentX you want the print head to have room for two
digits to the left of the start of the tic mark. For CurrentY you want the print head to print
out the digit half above the tic mark and half below the tic mark.
5. Write a program that draws on the screen two overlapping circles. One circle should be solid
red and the other should be solid blue
6. Write a program to draw a histogram with six vertical bars. The values represented are 25,
60, 85, 70, 90, and 55. Use two pixels of height to represent each unit. The categories should
be labeled cars(25%), trucks (60%), SUV (80%), ATM (70%), Hogs (90%), and bikes (55%).
7. Repeat problem 6 but use horizontal bars for display.
8. Write a program that draws a pie chart with three regions. The regions represent 60%, 30%,
and 10% of the circle. Draw the sector for the largest sector so that it pulled out of the circle.
We call this an exploded sector.

199
Arrays and Tables
10 Arrays and Tables
Programs to this point have input data for immediate use. We have not needed to use a piece of data
entered a second time after some major computation step involving all the data values is completed. There
are, however, instances such as finding all the scores greater than the average of the set of scores that
cannot be solved by making a decision when a value is entered. In many problems that require finding
how data values relate to some computed property, we need to process the data once to determine the
property and then go through each data value again to compare it with the property. Certainly, we could
reenter the data but that is both tedious and error prone. We could also use a different variable name for
each data value so it would remain in memory after its use. Using different names for each data value
leads to unnecessarily long programs that are also tedious to write and very error prone for the user.
What we want is a convenient way to store any number of values of the same data type in memory and
be able to reuse the values easily.
Figure 10-1 shows the output of a statistical analysis program.

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Figure 10‑1: Statistical Analysis of Sample
A simple example of finding the values greater than the average using three values is shown in Figure
10-2. Just think of how this program would be written if there were thousands of data values.

200
Arrays and Tables
Rem INPUT: Three numbers
Rem OUTPUT: The average of the numbers and
Rem the numbers greater than the average
sum = 0
A grade1 = Val(InputBox(“Enter first number:”))
sum = sum + grade1
grade2 = Val(InputBox(“Enter second number:”))
sum = sum + grade2
grade3 = Val(InputBox(“Enter third number:”))
sum = sum + grade3
B Rem Find average
ave = sum / 3
Print ave
C If grade1 ave Then
Print grade1
End If
If grade2 ave Then
Print grade2
End If
If grade3 ave Then
Print grade3
End If
Figure 10‑2: Finding Values Greater Than the Average for Three Data Values
In Figure10-2 the code starting with A enters three data values and assigns each to a separate storage
location. The storage locations are named grade1, grade2, and grade3. The data values are added together
as they are entered as this is required to find the average. In B the summing is finished and the average
is calculated. In C the program must revisit each of the data values to determine if it is greater than the
average.
10.1 Defining an Array
In the example above we needed to store three values that each represented a grade. Each value was
assigned to a separate storage location by means of the variable names used. For sets of data values that
are of the same kind, such as, grades, names, tax rates, BASIC allows the programmer to name a storage
area consisting of any number of storage locations each of which can be used for similar kinds of data.
Such a storage area is called an array. For the example in Figure 10-2, we need a storage area with three
storage locations as shown in Figure 10-3.

201
Arrays and Tables
grades
Figure 10‑3: Storage Area Named grades
There is still one problem to solve. How do we reference a single one of these storage locations? Remember
grades is the name of all this storage. To differentiate the individual storage locations, BASIC simply
numbers the storage locations allocated when the storage area is defined. Normally, the numbering of
the storage locations begins with 1 and proceeds from left to right giving each other storage location a
number one more than its left neighbor. The number of the storage location is called a subscript. We
now have a model for grades that looks like the one in Figure 10-4.
grades
1 2 3
Figure 10‑4: grades with Subscript Numbering
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202
Arrays and Tables
10.2 The Syntax of Defining Arrays
To use arrays and subscripts to reference a storage location and/or its contents BASIC uses a two part
syntax. The first part of the syntax explained here is the statement used to allocate a storage area with
properly numbered storage locations. In addition the programmer must tell what kind of information
(Integer, Single, Double, or String) will be put in each location in the array. All locations in an array
must be used for the same kind of data value. Integer values are whole numbers between -32768 and
32767. A Double value is any numeric value that is to be treated as if it contained a decimal point. Both
35 and 35.0 are examples of values of type Double. The value 35 could also be considered of type Integer
but 35.0 could only be considered of type Double. Single is a less flexible data type than Double that
also deals with numeric values containing a decimal point. The syntax for defining an array is:
SYNTAX
Array-Dim Statement
Dim arrayName (num1 To num2) as dataType
arrayName : valid variable name
num1, num2: range of array-subscript range with num1 num2
dataType Integer, Single, Double, or String
EXAMPLE: Dim grades (1 To 10) as Double
x = grades(2)
Many times the program will allocate more storage locations than needed for a particular instance of
a problem. It will make no difference to BASIC and the program will have the flexibility to be used for
different number of data items without having to change the program. The program is responsible to
keep track of how many storage locations are used regardless of how many are in the range of the array.
Of course, the program cannot try to use more storage locations than are allocated.
10.3 Assigning and Using Values in an Array
In the last section we saw how to allocate a block of memory with a number of storage locations for
holding values of the same type. There were two key parts to the definition. The first was the name of the
whole area allocated. The name for an array is formed following the rules for making a variable name. We
must now see how BASIC accesses a particular one of the storage locations in the area defined in a Dim
statement. The second part of the name for a location in an array is called a subscript and indicates which
location in the array is being referenced. A subscript is included in parentheses following the array name.

203
Arrays and Tables
SYNTAX
Array Elements
Dim variable (num1 To num2) as dataType
Individual elements are accessed using a two-part name. The
first is the name of the storage area. The second is the number
of the particular location in the array being referenced written in
parentheses following the array name. The result is a variable name.
EXAMPLE: Dim grades (1 To 10) as Double
grades (2)
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204
Arrays and Tables
An example using array elements is shown in Figure 10-5. BASIC automatically initializes storage
locations in arrays containing numeric values to zero.
Dim cost (1 To 5) as Double
cost
0 0 0 0 0
1 2 3 4 5
Assigning Values: cost(1) = 3.86
cost(2) = 4.71
cost(4) = 3.98
cost
3.86 4.71 0 3.98 0
1 2 3 4 5
Using Values: total_cost = 75 * cost(2 ) = 75 * 4.71
ave_cost = (cost(1) + cost(2) + cost(4))/3
= ( 3.86 + 4.71 + 3.98) /3
Figure 10‑5: Using Array Elements
A variable name indicating a location in an array is really no more than a variable name with a slightly
different format because of the subscript. The advantage to an array is that it is easy to access each of
its values by merely changing the value of the subscript. The program in Figure 10-6 shows how arrays
can be used with a For .. Next loop

205
Arrays and Tables
Dim surName (1 To 10) as String
Dim carModels (1 To 20) as String
N1 = Val(InputBox(“# surnames”))
For I = 1 To N1
surName(I) = InputBox(“Enter surname:”)
Next I
N2 = Val(InputBox(“# car models”))
For I = 1 To N2
carModels (I) = InputBox(“Enter car model:”)
Next I
Rem Print selected car models surNames
Print “Output car models”
For I = 1 To N2 Step 3
Print carModels(I)
Next I
Print “Output surnames”
For I = 1 To N1 Step 2
If surName(I) “M”Then
Print surName(I)
End If
Next I
Figure 10‑6: Arrays and For..Next
On Your Own
1. Allocate a storage area with seven locations numbered 10, 11, … , 16.
2. Allocate a storage area with ten locations numbered 0, 1, 2, … , 8, 9.
3. Allocate a storage area with eight locations numbered 2, 3, …, 9. Assign 1, 3, 5, 7, 9, 11, 13,
and 15 to these locations starting with 1 in location 2.
4. Allocate a storage area with seven location numbered 1, 2, … , 7 with 3* location number as
an initial value.
10.4 Finding the Average and the Standard Deviation
Now that we have the tools to use an array, it is instructive to see how the program we used to introduce
the idea of an array can be written using this new feature. The program similar to the program shown
in Figure 10-2 is shown in Figure 10-7. The difference is that this program uses both the average and
the standard deviation to identify special values.

206
Arrays and Tables
A Dim grade (1 To 10) as Integer
sum = 0 : sumSq = 0
N = Val(InputBox(“Enter Number of Grades”))
For I = 1 to N
B grade(I) = Val(InputBox(“Enter a grade”))
sum = sum + grade(I)
sumSq=sumSq + grade(I)^2
Next I
ave = sum / N : stDev = sqr(1/N* sumSq – ave^2)
Print “Grades “;ave + Stdev
For I = 1 To N
C If grade(I) ave + stDev Then
Print grade(I)
End If
Next I
Figure 10‑7: Grade Program Using an Array
In A the array is defined. Notice the program could be used for larger data sets as the array is defined
to contain ten locations numbered from 1 to 10. In B the program reads the data and stores each data
value in a different location in the array grade. The code also accumulates the values needed to compute
both the average and the standard deviation of the grades. Finally, in C the program revisits the elements
of grade to determine which of the values are larger than the average plus one standard deviation. (The
standard deviation measures how values cluster around the average.)
10.5 File Input
The model for using arrays to this point will normally require using InputBox() to assign values to
array locations each time a program is run to enter the data. With applications using arrays it is often
the case that there is a lot of data to process. Entering each data value using the InputBox() approach
is very time consuming and can be quite prone to error. To make dealing with large amounts of data
more convenient, a very restricted version of file input will be shown. The model given can be used with
any program but is most useful with entering values into an array. The programs you write can take
the block of code that is introduced and just copy it into a program whenever file input is needed. The
only other problem to deal with is how to create a file for the data. A file can be created in Word if the
result is saved as having type txt. You can choose this file format option in Word in the Save As Type
pull down menu when you go to save the data file.

207
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For use in this book we use a very special format for the data files so the input code template is simpler.
The restriction on the format of a data file is that the first value must be the number of data items. The
data items follow one after another after the initial number of data items entry with each entry in the
file separated from the next (including the number of data items from the first data item) by a comma.
Suppose the data consists of five values: 4, 7, 5, 2, 9. The file would be created as:
5,4,7,5,2,9
and saved as filename.txt. The syntax and code used to enter a data file so that each value is in a different
location in an array has a different syntax from the InputBox() function.
SYNTAX
Read From A File
Open“filespec” for Input as #n
Input #n, N
For I = 1 To N
Input #n, dataValue(I)
Next I
Close #n
filespec: path name to file
n: an integer value
dataValue(): arrary and subscript
Close: releases the link from BASIC to the file
EXAMPLE: Open “PATHdataFile.txt”for Input as #1
Input #1, noElements
For I = 1 To noElements
Input #1, dataValue(I)
Next I
Close #1
The Open statement makes a connection between the data file and the BASIC program by telling the
program how to access the data file in the local file space. For purposes of our use the filename will be
of one of the forms:
netspacestudentsinitlogonpublicfilename.txt
netspacedepartmentscomputer_sciencepublicfilename.txt

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Arrays and Tables
In the first path, init is the first letter of your surname and the logon is your user name. The file filename.
txt will be whatever file is used in the program. Obviously, if you are not using this file system, you
will have to determine the filespec in terms of your computing environment. In Windows you can use
Windows Explorer to find the path you need BASIC to know. In general, the filespec will be shortened
as PATHfilename.txt where you will need to replace PATH with what is appropriate for your file system.
The code you will actually use to access the elements in a data file is shown in Figure 10-8.
Dim arrayName (1 To 100) as Double
Open “PATHdataFile.txt”for Input as #1
Input #1, N
For I = 1 To N
Input #1, arrayName(I)
Next I
Close #1
Figure 10‑8: Code to Enter Data into an Array from a File
The block of code shown in Figure 10-8 can be used for any array input operation needed by just forming
PATH and using the appropriate dataFile.txt name. Once the PATH is used in the Open statement, it is
not referenced again in the program.

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10.6 Using Arrays – Searching an Array
Once an array is assigned values, a common operation for a user to request is to find out if some value
is in one of the array locations. This operation is called searching an array. The code to carry out the
search of an array is shown in Figure 10-9.
Rem Determine if a value is stored in an array and returns its location if found
Rem INPUT: An array with N elements and and a value to search for
Rem OUTPUT: The location of the element in the array or message “NOT FOUND”
A Dim elements (1 To 100) as Double
Input #1, N
For I = 1 To N
Input #1, elements(I)
Next I
B Close #1
C searchElement=Val(InputBox(“Enter value to be found”))
location = -1
For I = 1 To N
D If searchElement = elements(I) Then
location = I
GoTo L1
End If
Next I
E L1: If location = -1 Then
Print searchElement; “ NOT FOUND.”
Else
Print searchElement; “ was found at location:”;location
End If
Figure 10‑9: Search Code
The code from A to B dimensions an array and reads a file into the array. The element that is the object
of the search is entered by the user at C. In D the program examines each entry in the array to see if any
of the elements match the element sought. The transfer to E when the element is found lets the program
avoid searching additional array locations when the answer is known. If the element is not found, after
the whole array is searched, control passes to E with location still having its initial value of -1.
10.7 Using Arrays – Finding a Smallest Element in an Array
Putting the elements in an array in increasing or decreasing order is called sorting. To understand a
simple sorting program, there are two parts of the process that need to be explained. In this section we
examine the problem of finding the smallest element in some range of subscripts. In the next two sections
we finish our exploration of sorting. In Figure 10-10 we show how to find a smallest element in an array.

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Rem Find the smallest element in an array
Rem INPUT: The number of string elements and the strings
Rem OUTPUT: The smallest value in the array
A Dim stringElements (1 To 100) as String
B Open “PATHdataFile.txt”for Input as #1
Input #1, N
For I = 1 To N
Input #1, stringElements(i)
Next I
C Close #1
D smallest = 1 ‘first estimate of location of answer
For I = 2 To N
If stringElements(smallest) stringElements(I) Then
smallest = I
End If
E Next I
F Print smallest, stringElements(smallest)
Figure 10‑10: Finding a Smallest Element
In A the program defines an array which can hold up to 100 elements of type String. A file of elements
is identified and its elements are input into the array in the code from B to C. The code from D to E
compares each element successively in the array with the smallest element encountered to that point. If
an element is found that is smaller than the smallest to that point, we update the location of the smallest
element encountered so far. When we get to F, the location in smallest gives the location of the smallest
element in the array. The smallest means the least element in the array as determined by the ordering
relation on that type of element. The ordering could be either the natural numeric ordering for numbers
or the dictionary ordering for strings.
10.8 Using Arrays – Interchanging Two Elements in an Array
In the process of sorting we first find the smallest element in the array and then interchange it with the
element in the first location. When we finish, the smallest element is in the first location of the range
searched and the original element in that location is now in the location that originally contained the
smallest element in the range. Figure 10-11 shows the general process of interchanging two elements in
an array where one is located location J = 2 and the second at location K = 5. Interchanging two elements
need not involve the smallest element in a range of subscripts as we see in this example.

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Arrays and Tables
YDOXHV
25,*,1$/

- .
YDOXHV
$)7(5,17(5+$1*(

- .
Figure 10‑11: Interchanging Two Elements in an Array
To interchange two elements in an array, we must know the location of each of the values, say J and K.
It is tempting to write the following code to interchange the elements at these two locations:
elements(J) = elements(K)
elements(K) = elements(J)
If we trace this code for the original values:
elements(J) = 18
elements(K) = 9
we first assign elements (K) to elements (J) giving
elements(J) = 9
If we now assign elements(J) to elements(K) we get
elements(K) = 9.
The difficulty arises because the value of elements(J) is changed to the original value in elements(K)
before we assign the contents of elements(J) to elements(K). The solution to the problem of actually
interchanging two elements is to assign the original value of elements(J) to a separate variable before
we assign the value in elements(K) to elements(J). We can then assign the value in the separate variable
to elements(K) and get the two elements interchanged as we intended. The code to solve this problem
is shown in Figure 10-12.

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Arrays and Tables
Rem Interchange two elements in an array. Print the array before
Rem and after the interchange
Rem INPUT: An N element array and two locations of elements
Rem to interchange
Rem:OUTPUT: The array before and after the interchange
A Dim elements (1 To 100) as Integer
For I = 1 To N
Input #1, elements(I)
Next I
Close #1
B For I = 1 To N
Print I, elements(I)
Next I
C J=Val(InputBox(“First interchange location”))
K=Val(InputBox(“Second interchange location”))
Print J,elements(J), K, elements(K) ‘original places for elements
D temp = elements(K)
elements(K) = elements(J)
elements(J) = temp
Print J,elements(J), K, elements(K) ‘see what has changed
E For I = 1 To N
Print elements(I)
Next I
Figure 10‑12: Interchanging Two Elements in an Array
Starting at A the array is defined and the file of elements is read into the program. The loop starting at
B is simply a printing of the elements in the original order. The two values entered at C are the array
locations whose elements need to be interchanged. In the code starting with D the actual interchange
takes place. Notice the use of the variable temp. The loop starting at E prints the array with the two
elements interchanged.
10.9 Using Arrays – Sorting an Array
For the sorting process we will use a simple algorithm that has two major steps that are repeated. The
two steps are first to find the smallest element in a range of storage locations and then interchange
that smallest value found with the first element in that range of locations. Since we build up a sorted
array one element at a time, we will need to repeat this process with an increasingly smaller number of
elements in the search area until all the elements are in sorted order. The coding tool we use is a nested
For .. Next construct.

213
Arrays and Tables
For the sorting process we first need to find the smallest element in the array and put that element in
location 1. The second step is to find the smallest value remaining in locations 2, 3, … , N and put that
element in location 2. The key is to have a smaller range of locations to search each step so previously
found smallest elements are not found again! We show an example for an array with four elements in
Figure 10-13.
Figure 10‑13: Minimum Selection Sorting Example

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Arrays and Tables
The code that actually carries out the sorting is shown in Figure 10-14.
Rem Sort an array with N elements
Rem INPUT: The number of elements in an array and the elements
Rem OUTPUT: The N elements of the array in increasing order
Dim values (1 To 100) as Double
Input #1, N
For I = 1 To N
Input #1, values(I)
Next I
Close #1
A For I = 1 to N – 1
smallLocation = I ‘first estimate of location ofanswer
For J = I + 1 to N
B If values(J) values(smallLocation) Then
smallLocation = J
End If
Next J
temp = values(I)
C values(I) = values(smallLocation)
values(smallLocation) = temp
Next I
For I = 1 To N
D Print values(I)
Next I
Figure 10‑14: Minimal Selection Sort
In A we set the loop control so that the minimal search process is repeated N – 1 times. When I = N-1
we are comparing the elements at N-1 and N. When this loop is finished both of these elements are in
increasing order. Consequently, we do not have to repeat the body of the loop when I = N. (There are
no elements in locations past location N so the element in location N is the smallest element in the
range of N to N!!) B is looking for the smallest element in the range I + 1, …, N as we start the process
saying that the smallest element is in location I. We update out estimate of the location of the smallest
element by comparing each element in the search range with the best estimate found to that point of
the search. When I = 1, we compare elements at 2, 3, … , N. When I = 2, we compare elements at 3,
4, … , N. As I increases, the number of elements in the search range decreases. The interchange that
puts the smallest element in location I is carried out at C. In D the array has its elements printed out
after the sort is completed.

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Arrays and Tables
10.10 Using Arrays – Finding a Distribution of Elements
Since arrays are used to store many data values, it is often useful to find out how the data is distributed
over the range of all the data. This idea is used to find out how many values fall in each bracket of a
decomposition of the range of values. There are several ways we can define the brackets of a decomposition
for integer values. In this example we are looking for how many values in an array with elements in the
range 0-100 are in each of the following intervals:
Brackets
88–100 80–87 73–79 60–72 0–59
1 2 3 4 5
Table 10-1: Brackets for a Distribution
The brackets are given and can be quite different for different applications and different data sets. One
method to find out how many values are in each bracket uses the Multi Case If . The selection code is
shown in Figure 10-15 with the bottom value of Brackets(I) in elements where I ranges from 1 to 5. The
number of elements in a bracket is counted in the array categories.

216
Arrays and Tables
For I = 1 To N
If elements (I) =88 Then
categories(1)=categories(1)+1
ElseIf elements (I) = 80 Then
Else
End If
Next I
Figure 10‑15: Multi Case If Categorization of Data
The If .. ElseIf statement is really quite involved. If a value is found to be less than 88, it will be compared
with 80. The interesting aspect to this syntax is that if the comparison with 88 is false, we know that
the element is not in the interval 88–100. This means the next condition is true if the element is in the
interval 80–87 even though it looks like we are asking if the value is in the range 80–100. Checking on
the upper bound for an interval is unnecessary but is implied since the conditions ask about the bottom
value in a bracket having eliminated all brackets above the one with this bottom value.
A second alternative used for finding a distribution uses a sequence of compound conditions to determine
the categories. The code for this approach is shown in Figure 10-16.
For I = 1 To N
If elements (I) =88 Then
End If
If elements (I) = 80 And elements (I) = 87Then
End If
If elements (I) = 73 And elements(I) =79Then
End If
If elements (I) = 60 And elements(I) =72Then
End If
If elements(I) = 59 Then
End If
Next I
Figure 10‑16: Selection Using Compound Conditions

217
Arrays and Tables
10.11 Using Arrays – Parallel Arrays
Problems using arrays have focused on computing with a single set of related values. Even with the
problem of finding the average of a set of numbers, there is often other information related to each value
that must be used in the problem solution. For example, suppose a set of grades is stored in an array
named grades and the corresponding set of student names is to be stored in an array named student. To
find the name of the student with the highest grade requires we know which grade belongs to which
student. It is certainly possible to have one array store the grades and another array store the names. The
issue is that if location I in grades contains a grade that it should be easy to find the name of the student
whose grade it is. The simplest solution is to enter a grade and a name so that the subscript used to
identify the location in grades is also used to identify the location in student where that student’s name
will be stored. The process of coordinating the use of storage locations in two or more arrays is known
as using parallel arrays.
+ in + + ity
the of th + - c
- ste

218
Arrays and Tables
The problem solved in Figure 10-2 can be expanded using parallel arrays to identify not only the grades
greater than the average but also the names of the students with a grade greater than the average. See
Figure 10-17.
Dim student (1 To 50) as String
Dim grade (1 To 50) as Integer
sum = 0 ‘accumulator
N = Val(InputBox(“Enter number of values.”))
For I = 1 to N
student(I) = InputBox(“Enter student’s name:”)
grade(I) = Val(InputBox(“Enter a grade”))
sum = sum + grade(I)
Next I
ave = sum / N
For I = 1 To N
If grade(I) ave Then
Print student(I),grade(I)
End If
Next I
Figure 10‑17: Using Parallel Arrays for Grades and Names
10.12 Using Arrays – Drawing A Pie Chart
The tools we learned in Chapter 9 about drawing capabilities in BASIC can be used in more complex
problems when we use arrays. The problem of displaying data using a pie chart is modified here by using
an array to keep track of the size of each sector in terms of the percentage of the total area of the circle.
Example 10‑1. Write a program that creates a pie chart with three sectors. The user enters the size of
two sectors, and the chart is created based on that data.
SOLUTION:
The sector sizes have been input to be 20% and 35%. The third sector will have size 100 – 20 – 35%.

219
Arrays and Tables
Rem Create a pie chart with three sectors. The size of
Rem the sectors are based on the user’s data.
Rem INPUT: Percent of circle representing size of some sectors
Rem OUTPUT: A pie chart with three sectors
Dim sector (1 To 10) as Double
Cls
Rem Get input
A For I = 1 To 2
sector(I) = Val(InputBox(“Enter sector size:”))
Next I
sector(3) = 100 – sector(1) – sector(2)
Rem Initialize variables
B pi = 3.14159
radius = 80
stopangle = .001
Rem Draw each sector
C For I = 1 To 3
If I = 1 Then
FillStyle = 3
FillColor = vbBlue
ElseIf I = 2 Then
FillStyle = 5
FillColor = vbGreen
Else
FillStyle = 7
End If
Rem Calculate position and size of current sector
D angle = 2 * pi * sector(I)/100
E startangle = stopangle
stopangle = startangle + angle
If stopangle 2 * pi Then
stopangle = .001
End If
Rem Draw the sector
F Circle (160, 100), radius,,-startangle,-stopangle
Next I

220
Arrays and Tables
COMMENTS: The program begins by allowing the user to input two of the sector sizes at A. Beginning
in B, variables that will be used later are initialized. The For .. Next loop beginning in C draws each
sector individually. Within the loop, D merely computes the appropriate sector size to draw in radian
measure. Beginning in E, equations are used to calculate the size and position of the sector currently
being drawn. The Circle command at F actually draws the sector. The radius of the sector is the radius
that was initialized at B. The color and style of the sector is given by the values assigned to FillColor
and FillStyle in the If block beginning at C.
On Your Own
1. Write a program that creates a pie chart with four sectors. Let three of the sector sizes be
20%, 25%, and 15%. The fourth sector is the remaining portion of the circle. Use any colors
and fill styles.
10.13 Using Arrays – Drawing a Histogram
When values need to be seen in comparison to other values as the sales for a sequence of months or the
number of gyzmos sold each month, the chart often used is a histogram. A histogram represents a set of
values using as a scale the relative difference in the magnitudes. The output form shown here displays a
histogram for values collected over a period of four months denoted by J(anuary), F(ebruary), M(arch),
and A(pril). We see the output for this problem in Figure 10-18.
Figure 10‑18: A Histogram
The code to draw this chart is given in Example 10-2
Example 10-2. Draw a histogram representing the four values 120, 200, 90, and 250 that represent sales
in January, February, March, and April, respectively. Scale the values so that 120 is represented by 24,
200 by 40, 90 by 18, and 250 by 50. Use the labels J, F, M, A for the four months.

221
Arrays and Tables
SOLUTION:
Rem: Draw a histogram with four values
Rem INPUT: Four values to be represented
Rem OUTPUT: Histogram representing the relative size of the input numbers
Dim heightValue (1 To 10) as Integer
Dim label (1 To 10) as String
Line (100, 300) – (100, 100)
Line (100, 300) – (250, 300)
Rem Tic mark on the down axis-each tic represents 4 units
For I = 1 to 20
Line (98, 300 – 10 * I)-(102, 300 – 10 * I)
Next I
Rem Enter heights and labels
For I = 1 to 4
heightValue(I) = Val(InputBox(“Enter height”))
label(I) = InputBox(“Box label”)
Next I
Rem Draw and label rectangles
For I = 1 to 4
Line (120 + 30 * (I – 1), 300) – (140 + 30 * (I – 1), 300 – 3 * heightValue(I)), ,B
CurrentX = 125 + 30 * (I – 1) : CurrentY = 312
Print label(I)
Next I
1. Input five numbers into an array using a For .. Next loop. Then using another loop, print
the values in the array.
2. Read ten values into an array using a For .. Next loop. In a second For .. Next loop add
these numbers and finally print the average of the ten numbers.
3. Read N numbers from a file and store them in an array. Count the number of values that are
bigger than the average value.
4. Count the number of values that are less than the average minus 8, the number between
(inclusive) the average plus 8 and the average minus 8, and the number greater than the
average plus 8. Read the values from a file into an array. Use variables ct1, ct2, and ct3 to
store the counts. Print the number of values in each category.
5. Repeat problem 4 but store the counts in an array ave with three storage locations. Print the
values in ave using a For .. Next loop. Print the values on a single line.
6. Modify the code in Figure 10-17 so that there are three parallel arrays. The first array holds
the size of the sectors. The second array at the same index holds the FillStyle value for this
sector. The third array at the same index holds the FillColor value for this sector. Run the
program for a five sector pie chart.

222
Arrays and Tables
7. Modify the code in Example 10-2 so that up to seven bars can be included in the histogram.
Use parallel arrays for the bar heights and the bar labels. Use files for the input into the
arrays. Experimental data is often “smoothed” before it is used. The “smoothing” process
replaces each value by the average of the three points that precede it. For example, for a
data file with N elements in an array rawData a new array smoothData is defined and given
values as follows:
smoothData(1) = 0
smoothData(2) = 0
smoothData(3) = 9
smoothData(4) = (rawData(1) + rawData(2) + rawData(3)) / 3
In general,for 4 I N define
smoothData(I) = (rawData(I) + rawData(I – 1) + rawData(I – 2) / 3.
Write a program that smoothes data in a file with 25 random numbers in the range 0-18. Output
the results in a table with three columns with titles I, rawData(I), smoothData(I).
8. Experimental data is often “smoothed” before it is used. The “smoothing” process replaces
each value by the weighted average of the three points that precede it. For example, for a
data file with N elements in an array rawData a new array smoothData is defined and given
values as follows:
smoothData(1) = 0
smoothData(2) = 0
smoothData(3) = 9
smoothData(4) = (rawData(1) + rawData(2) * 2 + rawData(3) *3) / 3
In general, for 4 I N define
smoothData(I) = (rawData(I – 1) + rawData(I – 2) * 2 + rawData(I – 3) * 3) / 3.
Write a program that smoothes data in a file with 25 random numbers in the range 0-18. Output
the results in a table with three columns with titles I, rawData(I), smoothData(I).

223
Index
Index
algorithm, 27
alphabet, 78
ampersand (), 67
And, 88
arc, 185
arithmetic operations
order, 59
priority, 59
array, 200
distribution of elements, 215
parallel, 217
search, 209
smallest element, 209
ASCII-8, 78, 81
aspect, 189
assignment statement, 47
asterisk, 60
BackColor, 165
biased coin, 148
binary code, 78
body of the loop, 123
box, 179
box filled, 179
branching, 101
conditional, 101, 106
unconditional, 101, 102
built in function, 63
Abs(), 63
Exp(), 63
Int(), 153
Log(), 63
Mod, 99
Rnd, 142
Sqr(), 63
Cls, 31
code, 27
colon (:), 102
color, 176, 179
color constants, 164
give us a call on +44 (0)20 7000 7573.
The next step for
top-performing
graduates

224
Index
comma
end of Print statement, 34
comment, 28
comparisons, 75
numeric, 76
string, 78
compound condition, 88
concatenation, 67
condition, 84
conditional statement, 83
control variable, 123
range, 124
convention
coding, 29
spacing, 84, 127
counter, 123
currency, 69
CurrentX, 38
CurrentY, 38
data
numeric, 45
string, 45
data file, 207
data type, 202
Double, 202
Integer, 202
Single, 202
String, 202
decision making, 75
default position, 38
demand curve, 134, 135
dialog box, 49
dictionary ordering, 79
digits
left of decimal point, 69
right of decimal point, 69
Dim, 202
Dimension (Dim), 202
distribution of elements, 215
Double, 202
ellipse, 189
Else, 86
ElseIf, 93
encapsulation, 126
exponential notation, 68
expression, 45, 58
numeric, 45
parenthesised, 62
string, 45
false range, 86
FillColor, 190
FillStyle, 190
font_height, 38
font_width, 38
For .. Next loop, 121
ForeColor, 165
Format(), 68
$, 69
0, #, @, 70
comma, 69
currency, 69
percent, 70
standard, 70
GoTo, 102
histogram, 195, 220
I f.. Then .. End If, 83
If Then Else End If, 86
increment, 123, 129
indenting, 29
Int(), 153
Integer, 202
interchange elements, 210
keyword, 27, 46, 84
letters
lowercase, 81
uppercase, 81
Line, 176
line labels, 101
literal, 45
numeric, 45
string, 45
logical operations
And, 88
Not, 88

225
Index
Or, 88
looping, 121
marker, 84
Else, 85
End If, 84
For, 123
If, 84
Next, 123
Then, 84
To, 123
Mod, 99
negation, 60
non-executable, 28
normalized representation, 68
Not, 88
numeric data, 45
numeric variable, 45
numerical operation, 58
operations
concatenation, 67
hierarchy, 59
mathematical, 58
numerical, 58
priority, 59
operator (), 114
Or, 88
outcome
equally likely, 146
output display, 38
output form, 38
output menu, 54
parallel arrays, 217
parentheses, 61
pie chart, 163, 194, 218
pixel, 38, 163
Print, 51
comma, 34
positioning output, 38
semicolon, 33
print zone, 34
procedure, 27
prompt, 49
prompt and echo, 113
PSet(), 165
radius, 220
random number, 142
scaling, 153
Randomize, 144
range, 209
counter, 124
relational operator, 76
string, 82
relational operators, 76, 82
Rem, 28, 29
RGB(), 164
Rnd, 142
scaling, 153
scientific notation, 143
search an array, 209
sector, 188
seed, 144
semantics, 47
assignment, 47
branching, 108
Cls, 31
For .. Next, 121, 123
For .. Step .. Next, 129
GoTo, 102
If .. Then .. Else .. End If, 86
If .. Then .. ElseIf .., 95
If .. Then .. End If, 84
InputBox(), 49
repetition, 109
Val(), 53
variable name, 45
semicolon, 33
end of Print statement, 35
sentinel, 110
simulation, 158
Single, 202
single quote, 30
slope, 170
smallest element, 209, 210
sort, 209, 212

226
Index
statement
assignment, 47
comment, 28
Step, 128
string, 78
String, 202
string comparisons, 78, 82
string constant, 45
string data, 45
string variable, 45
subexpressions
arithmetic, 62
subscript, 201
subscript range, 202
supply curve, 134, 135
symbol overloading, 61
symbolic constant, 45
SYNTAX, 27
arc, 185
aspect, 190
assignment, 48
Circle, 183
Cls, 31
concatenation, 67
CurrentX, 40
CurrentY, 40
Dim(ension), 202
ellipse, 190
FillColor, 192
FillStyle, 192
Fo r.. Next loop, 122
For .. Next, 123
For..Next with step, 129
Format(), 68
GoTo, 102
If .. Then .. Else .. End If, 85
If .. Then .. ElseIf, 95
If .. Then .. End If, 84
Input, 207
InputBox(), 50
Line, 176, 179
line label, 102
Line..BF, 179
Open, 207
path name, 207
Print, 35
Pset ( , ), color, 166
Randomize, 145
Rem, 30
Rnd, 143
sector, 188
Val(), 54
variable name, 46, 203
true range, 84
truth table, 89
And, 89
Not, 90
Or, 90
user friendly interface, 41
user interrogation technique, 118
Val(), 53
value
boolean, 75
logical, 75
string, 45
variable, 45, 46
variable name, 45
window size, 34
word, 45, 78
zone, 34

227
Endnotes
Endnotes
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