Fundamental_of_Digital_Computer and its architecture

FUNDAMENTAL OF
DIGITAL
COMPUTERS
CSE4001

Objective:
• This module provides a foundation for all professional computer
personnel in computer technology and related topics, including
number systems, hardware, operating systems, systems software,
and system performance measurement.

Learning Outcomes:
On successful completion of this module, students should be able to:
• Explain the principles of the architecture and organization of
computer systems.
• Explain the fundamental aspects of all digital computers
• Explain the operating principles of computer peripherals.
• Relate the principles underlying operating systems and system
software.

• Today, the world is becoming digital, in which the uses of computers is
increasing day by day. In such a situation, it is necessary for everyone to know
about computer.
What is Computer???

• “A computer is an electronic device that will take some data as input, process it,
and gives output“. when any device fulfills these four conditions then that is a
computer.
• A computer is a machine that can be programmed to carry out sequences of
arithmetic or logical operations (computation) automatically.
-Wikipedia
• The computer was built to run applications and solve many difficulties through
hardware and software. It has ability to store, retrieve, and process data.
What is Computer???

Features of Computer
• Speed:
Computers can perform millions of calculations per second. The computation speed is extremely
fast.
• Accuracy:
Because computers operate on pre-programmed software, there is no space for human error.
• Diligence:
They can perform complex and long calculations at the same time and with the same accuracy.
• Versatile:
Computers are designed to be versatile. They can carry out multiple operations at the same time.
• Storage:
Computers can store a large number of data/ instructions in its memory, which can be retrieved at
any point of time.

Basic Components of Computer
• There are basically three important components of a computer:
1.Input Unit
2.Central Processing Unit(CPU)
3.Output Unit

Input Unit
• The input unit consists of input devices that are attached to the computer.
• A user input data and instructions through input devices such as a keyboard,
mouse, etc.
• The input unit is used to provide data to the processor for further processing.

Central Processing Unit (CPU)
• The CPU is called the brain of the computer because it is the control center
of the computer.
• The CPU has three main components.
1. Arithmetic Logic Unit (ALU)
2. Control Unit (CU)
3. Memory registers

Arithmetic Logic Unit
• ALU is the main component and fundamental building block of the CPU.
• It is a digital circuit that is used to perform arithmetic and logical operations.

Control Unit
• The Control Unit is a component of the central processing unit of a computer that
directs the operation of the processor.
• It instructs the computer’s memory, arithmetic and logic unit, and input and
output devices on how to respond to the processor’s instructions.
• In order to execute the instructions, the components of a computer receive signal
from the control unit.

Memory Registers
• A register is a temporary unit of memory in the CPU. These are used to
store the data, which is directly used by the processor.

Functions of Central Processing Unit
• Process data
• Control sequence of operations within the computers
• It gives command to all parts of a computer
• It control the use of the main memory in storing of data and instructions
• It provides temporary storage (RAM) and permanent storage(ROM) of data

Output Unit
• The output unit consists of output devices that are attached to the computer.
• It converts the binary data coming from the CPU to human understandable form.

• Computer hardware refers to the physical components that make up a
computer system.
• Hardware helps to facilitate any computing operations as well as taking
input and outputting or storing the computed results.
• There are four main computer hardware components:
1.Input Devices
2.Processing Devices
3.Output Devices
4.Storage Devices
Computer Hardware

Input Devices
• Input devices comprise of any devices that users need in-
order to give instructions to a computer and also used to
transfer data between computers.
• Input devices are classified according to the method they
use to enter data.
 Keying devices :
Devices used to enter data into the computer using a set of Keys
 Pointing Devices :
Devices that enter data and instructions into the computer using a
pointer that appears on the screen. The items to be entered are
selected by either pointing to or clicking on them

Input Devices
 Scanning Devices
Devices that capture an object or a document directly from the
source. They are classified according to the technology used to
capture data.
e.g. Scanners and Document readers

Processing Devices
• Processing is the core function of any computer. When a
computer receives data from an input device, this data must first
go through an intermediate stage before it is sent to an output
device.
• Processing is the intermediate stage where raw data is
transformed into information so that it can be outputted
meaningfully for the user.

Output Devices
• Output devices are devices that allow computers to send
data to other devices or to users.
• In general, the data that computers send to human users is
in forms that they can understand.

Storage / Memory Devices
• Memory devices are any devices that are capable of storing
information temporarily or permanently.
• There are two types of memory.
1. Primary memory
2. Secondary memory.

Uses of Hardware
• It establishes an effective communication mode in organizations to
improve their business standards.
• It automates the task and helps store huge chunks of data that can
benefit the organization or individual.
• The user can give the command or instructions to the hardware,
which will obtain the output as per the given instruction.
• The fast processing speed of a hardware device is useful for
executing more operations at one time.
• Hardware devices are multiprocessing, meaning the user can use
more than one hardware device simultaneously.
• Installation and upgradation of the hardware devices in a computer
system are easy as per the user’s requirements.

• Software is a set of instructions, data or programs used to operate
computers and execute specific tasks.
• In other words, the software is a computer program that provides a set of
instructions to execute a user’s commands and tell the computer what to
do.
For example like MS-Word, MS-Excel, PowerPoint.
Computer Software

• System software is a type of computer program that is designed to run a
computer's hardware and application programs.
• Features of System Software
 System Software is closer to the computer system.
 System Software is written in a low-level language in general.
 System software is difficult to design and understand.
 System software is fast in speed(working speed).
 System software is less interactive for the users in comparison to
application software.
System Software

Type of System Software
• Operating System :
 It is the main program of a computer system.
 It manages all the resources.
 It provides an interface to the user, which helps the user to interact
with the computer system.
 It provides various services to other computer software.

Type of System Software
• Language Processor :
 System software converts the human-readable language into a machine
language and vice versa. So, the conversion is done by the language
processor.
• Device Driver :
 A device driver is a program or software that controls a device and
helps that device to perform its functions.

Application Software
• Software that performs special functions or provides functions that are much more
than the basic operation of the computer is known as application software.
• In other words, application software is designed to perform a specific task for end-
users.
• It includes word processors, spreadsheets, database management, inventory,
payroll programs, etc.

Features of Application Software
• An important feature of application software is it performs more specialized tasks
like word processing, spreadsheets, email, etc.
• Mostly, the size of the software is big, so it requires more storage space.
• Application software is more interactive for the users, so it is easy to use and design.
• The application software is easy to design and understand.
• Application software is written in a high-level language in general.

Types of Application Software
• General Purpose Software :
 This type of application software is used for a variety of tasks and it is not
limited to performing a specific task only.
For example, MS-Word, MS-Excel, PowerPoint, etc.

• Customized Software :
 This type of application software is used or designed to perform specific task
or functions or designed for specific organizations.

• Utility Software:
 This type of application software is used to support the computer
infrastructure.
 It is designed to analyze, configure, optimize and maintains the system, and
take care of its requirements as well.
For example, antivirus, disk fragmenter, memory tester, disk
repair, disk cleaners, registry cleaners, disk space analyzer, etc.

System VS Application Software

Types of Computers
•Computers can be classified into several types based on their sizes. Here are the
main categories:
1. Supercomputers:
• These are the most powerful computers in terms of processing capacity
and speed.
• They are used for complex scientific calculations, weather forecasting,
and simulations.
2. Mainframe Computers:
• Mainframes are large and powerful systems used by large organizations
for bulk data processing, such as census, industry and consumer
statistics and financial transaction processing.

Types of Computers
3. Minicomputers:
• Also known as mid-range computers, minicomputers are smaller than mainframes but
larger than microcomputers.
• They are used in manufacturing processes, research laboratories, and small businesses.
4. Microcomputers:
• These are the most common type of computers, also known as personal computers.
• They are used by individuals and businesses for everyday tasks such as word
processing, internet browsing, and gaming.
5. Servers:
• Servers are computers designed to provide services to other computers over a network.
• They can vary in size from small servers used in homes and small businesses to large
servers used in data centers.

Types of Computers
• Embedded Systems:
• These are specialized computers embedded within other devices, such as
appliances, cars, and medical equipment.
• They are designed to perform specific tasks and are not typically used as
general-purpose computers.

Number System
• In digital electronics, the numbers are used to represent the information
• A computer can understand the positional number system.
• It is important to learn and understand different types of number
systems so we can easily represent and interpret the information in the
form of numbers.
• In computer memory , numbers will represent in different formats.
Memory will support mainly 4 representation.
1. Decimal Number format
2. Binary Number format
3. Octal Number format
4. Hexa Decimal Number format

• The system of numbers which has base or radix 10 and it uses total 10 symbols to
represent numbers of the system is called decimal number system.
• The symbols used in the decimal number system are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
• The decimal number system is a position value system.
• Lets consider the decimal representation of 1234.
 Step 01:
 Step 02:
 Step 03:
Decimal Number System

• A number system with base or radix 2 is called binary number system.
• The binary number system uses only 2 symbols (0 and 1) to represent binary
numbers.
• All modern digital devices like computers, combinational circuits, sequential circuits,
etc. use the binary number system to operate.
• Lets consider the binary representation of 11012.
 Step 01:
 Step 02:
 Step 03:
Binary Number System

• A number system which has base 8 is called an octal number system.
• Therefore, the octal number system uses 8 symbols, (0, 1, 2, 3, 4, 5, 6, 7) to represent
the number.
• Lets consider the octal representation of 1248.
 Step 01:
 Step 02:
 Step 03:
Octal Number System

• The number system with base or radix 16 is called as hexadecimal number system.
• Thus, the hexadecimal number system uses 16 symbol to represent numbers.
• These symbols are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F. Where, A = 10; B = 11;
C = 12; D = 13; E = 14; F = 15.
• The hexadecimal number system is extensively used in microprocessors and
microcontrollers. Lets consider the hexa decimal representation of 1AF16.
 Step 01:
 Step 02:
 Step 03:
Hexadecimal Number System

Number System Conversion
• There are many methods or techniques which can be used to convert numbers
from one base to another.

Signed and Unsigned Binary Numbers

Unsigned Binary Numbers
• Unsigned numbers don't have any sign for representing negative numbers. So the
unsigned numbers are always positive.
• There is no sign bit in unsigned binary numbers so it can only represent its
magnitude.
• The range of the unsigned binary numbers starts from 0 to (2n
-1).
• Example: Represent the decimal number 102 in unsigned binary numbers.

Signed Binary Numbers
• The signed numbers have a sign bit so that it can differentiate positive and negative
integer numbers.
• The signed binary number technique has both the sign bit and the magnitude bit of
the number.
• The signed numbers are represented in three ways.
1. Sign-Magnitude form
2. 1's Complement
3. 2's Complement

1. Sign-Magnitude form
• In this form, a binary number has a bit for a sign symbol.
• If this bit is set to 1, the number will be negative else the number will be positive if
it is set to 0.
• Apart from this sign-bit, the n-1 bits represent the magnitude of the number.
2. 1's Complement
• By inverting each bit of a number, we can obtain the 1's complement of a number.
• The negative numbers can be represented in the form of 1's complement. In this
form, the binary number also has an extra bit for sign representation as a sign-
magnitude form.
• One of the main advantages of One’s Complement is in the addition and subtraction
of two binary numbers.

3. 2's Complement
• To find the 2's complement of the binary number, we will first find the
1’s complement of the binary number and then add 1 to the least
significant bit of it.
• Two’s complement is one’s complement + 1.
• The range of 2’s complement for n bit is from -2n-1
to 2n-1
-1.
• The main advantage of two’s complement over the previous one’s
complement is that there is no double-zero problem.
• Arithmetic operations are relatively easier to perform when the numbers
are represented in the two’s complement format.

Logical Gates
• A logic gate is a device that acts as a building block for digital circuits.
• They perform basic logical functions that are fundamental to digital circuits.
• Most electronic devices we use today will have some form of logic gates in them.
• Types of basic logic gates.
• OR
• AND
• NOT
• XOR

Truth Table
• The truth table is a systematic representation of all truth values of a logical
expression.
• It consists of all the inputs and gives the required output.
• Truth tables are mainly used in Boolean algebra so, a variable can take two
values 0 or 1.
• The truth table is primarily used in digital circuits where it is used to validate
the output generated from the various input combinations of the logical
expressions.

Usage of Logical Gates
1.Logic gates are utilized in a variety of technologies. These are components of
chips (ICs), which are components of computers, phones, laptops, and other
electronic devices.
2.Logic gates may be combined in a variety of ways, and a million of these
combinations are necessary to make the newest gadgets, satellites, and even robots.
3.Simple logic gate combinations can also be found in burglar alarms, buzzers,
switches, and street lights. Because these gates can make a choice to start or stop
based on logic, they are often used in a variety of sectors.
4.Logic gates are also important in data transport, calculation, and data processing.
Even transistor logic and CMOS circuitry make extensive use of logic gates.

Boolean Algebra
• Boolean algebra can be considered as an algebra that deals with
binary variables and logic operations.
• Boolean Algebra is used to analyze and simplify the digital (logic)
circuits.
• The Boolean algebraic functions are mostly expressed with boolean
variables, logic operation symbols, parentheses, and equal sign.
• The table used to represent the Boolean expression of a logic gate
function is commonly called a Truth Table.

Rule in Boolean Algebra
• Variable used, can have only two values. Binary 1 for HIGH and Binary 0 for LOW
• Complement of a variable is represented by an overbar (-).
• ORing of the variables is represented by a plus (+) sign between them.
• Logical ANDing of the two or more variable is represented by writing a dot between
them such as A.B.C. Sometime the dot may be omitted like ABC.

Boolean Function
• The logic diagram for the Boolean function F = x + y'z can be represented as:

Truth Table for Boolean function

Laws of Boolean Algebra
1. Commutative Law
2. Associative Law
3. Distributive Law

Laws of Boolean Algebra
4. AND Law
5. OR Law
6. Inversion Law

Boolean Algebra Theorems
• The two important theorems which are extremely used in Boolean algebra are De
Morgan’s First law and De Morgan’s second law.
1. De Morgan’s First law
• The first law states that the complement of the product of the variables
is equal to the sum of their individual complements of a variable.

Boolean Algebra Theorems
2. De Morgan’s second law
• The second law states that the complement of the sum of variables is
equal to the product of their individual complements of a variable.

Summary of Boolean Algebra Laws

Fundamental_of_Digital_Computer and its architecture

Logic Simplification With Karnaugh Maps
• We can minimize Boolean expressions of 2, 3, or 4 variables very easily
using the K -map without using any Boolean algebra theorems.
• We fill the grid of K -map with 0’ s and 1’ s then solve it by making
groups.
• The K-Map fill order

• K-map can take two forms:
• Sum Of product (SOP)
• Product Of Sum (POS)
• SOP
• SOP is one way of expressing a Boolean function.
• It represents a logical expression as a sum (logical OR) of product
(logical AND) terms.
• These product terms are also known as minterms.
• Minterms are formed by multiplying Boolean variables (either in
normal or complemented form).
• SOP is useful for simplifying complex Boolean expressions.

• Given three variables A, B, and C:
• Minterm for A=0, B=0, C=0: A′B′C′
• Minterm for A=1, B=0, C=1: A.B′C
• SOP Truth Table: X=A′B′C+A′B.C+A.B.C′

• POS (Product of Sums):
• POS is another way of expressing a Boolean function.
• It represents a logic function as a product (logical AND) of sum
(logical OR) terms.
• These sum terms are also called maxterms.
• Maxterms are formed by summing Boolean variables.
• Example of POS:
• Given three variables A, B, and C:
• Maxterm for A=0, B=1, C=0: A+B′+C
• Maxterm for A=1, B=1, C=1: A′+B′+C′
• POS Truth Table: X=(A+B′+C) (A′+B′+C′)
⋅

• The Karnaugh map uses the following rules for the simplification of
expressions by grouping together adjacent cells containing ones
1. No zeros allowed.
2. No diagonals.
3. Only power of 2 number of cells in each group.
4. Groups should be as large as possible.
5. Everyone must be in at least one group.
6. Overlapping allowed.
7. Wrap around is allowed.
8. Get the fewest number of groups possible

1. What will be the simplified expression for the given K-Map?
2. A boolean function is given as F(X,Y,Z) = Σ(1, 3, 6, 7).What is its
equivalent canonical form?
3. Minimize the following boolean function-F(A, B, C, D) = Σm(0, 1, 2, 5, 7,
8, 9, 10, 13, 15).

Simple Logic Gates – Full Adder
• A full adder is a digital circuit used in digital electronics and computer engineering
to perform binary addition.
• It takes in three binary inputs: A, B, and Cin (carry-in), and produces two outputs:
Sum (S) and Carry-out (Cout).
• The full adder is a fundamental building block in arithmetic circuits and is used to
add two binary numbers, taking into account any carry from the previous bit.
• Truth table for a full adder:

Simple Logic Gates – Full Adder
• Logical expression for sum = A XOR B XOR Cin
Cout = (AAND B) OR (B AND Cin) OR (AAND Cin).
• A full adder circuits are used in various applications, including arithmetic operations
in microprocessors, calculators, and digital signal processors.
• This circuit is a fundamental component in the design of digital computers and plays
a crucial role in performing arithmetic operations like addition, subtraction (using 2's
complement representation), and other more complex operations.

Multiplexer
• A multiplexer is a digital circuit that is used to select one of many input data lines
and route it to a single output line.
• Multiplexers are widely used in digital electronics and are an essential building block
in various applications, including data routing, data selection, and data transmission.
• A multiplexer has the following key components:
• Data Inputs(D0 , D1, D2)
• These are the multiple input lines from which you want to select one signal
to be routed to the output

Multiplexer
• Control Inputs(S0 , S1)
• These are the control lines that determine which input line is selected.
• The number of control inputs and the number of input lines are related by the
formula: Number of control inputs = log2(Number of input lines).
• Output
• This is the single output line to which the selected input is connected

Multiplexer
• Multiplexers are versatile components in digital circuit design and used in various
applications, including data routing, memory address decoding, and building complex
digital systems.
• Multiplexers are often used in combination to create larger multiplexers.
Applications of Multiplexers:
• Data routing and selection in digital systems.
• Memory address decoding in microcontrollers and microprocessors.
• Communication systems to switch between multiple data sources.
• Arithmetic logic unit (ALU) operation in CPUs.
• Reducing the number of pins required in integrated circuits (ICs).
• Building combinational logic circuits for various purposes.

Shift register
• A shift register is a digital circuit that can store and shift binary data (0s and 1s)
serially.
• It is often used for various applications in digital electronics, such as data storage,
data manipulation, and data transfer.
• A shift register consists of a chain of flip-flops interconnected in a way that allows
data to be shifted from one flip-flop to the next in a controlled manner.
• There are several types of shift registers.

Types of Shift register
• Serial-In, Parallel-Out (SIPO) Shift Register:
• In a SIPO shift register, data is input serially but is read out in parallel.
• It has multiple parallel output lines, and each flip-flop in the register
stores one bit of the serial input.
• Once all bits are loaded, they can be read out simultaneously.

• Serial-In, Serial-Out (SISO) Shift Register:
• This type of shift register has a single data input and a single data
output.
• Data is entered serially, one bit at a time, and is shifted through
the register one bit at a time.

• Parallel-In, Serial-Out (PISO) Shift Register:
• A PISO shift register accepts parallel data inputs but shifts it out serially.
It has multiple parallel data inputs and a single serial output.

• Parallel-In, Parallel-Out (PIPO) Shift Register:
• This type of shift register has both parallel input and parallel output lines. Data
can be loaded into all the flip-flops simultaneously and read out in parallel as
well.

• Bidirectional Shift Register:
• A bidirectional shift register can shift data in both directions, either to the right
(shift right) or to the left (shift left). It has additional control lines to determine
the shifting direction.

• They can be configured to respond to operations that require some form of
temporary memory storage or for the delay of information such as the SISO or
PIPO configuration modes or transfer data from one point to another in either
a serial or parallel format.
• Universal shift registers are frequently used in arithmetic operations to shift
data to the left or right for multiplication or division.

Shift register
• Shift registers are commonly used in various applications:
• Serial Data Transmission
• Data Storage
• Shift and Rotate Operations
• LED Displays
• Memory Expansion
• The behavior of a shift register depends on its configuration (SISO, SIPO,
PISO, PIPO) and the control signals applied to it.

Counter
• A counter is a digital circuit or device used in digital electronics to count events
or transitions in a digital signal.
• Counters are commonly used for a variety of purposes, including frequency
measurement, timekeeping, generating clock signals, and controlling sequential
logic circuits.
• Counters can be implemented using various types of flip-flops, and they come in
different configurations, such as binary counters, decade counters, and up/down
counters.

Counter
• Here are some common types of counters:
• Binary Counter
• Decade Counter
• Up Counter
• Down Counter
• Up/Down Counter
• Ring Counter

Counter
• Counters are used in various applications, including:
• Frequency Division
• Event Counting
• Timekeeping
• Sequential Logic
• Address Generation
Counters can be constructed using various types of flip-flops, such as D flip-flops,
JK flip-flops, or T flip-flops. The choice of counter type depends on the specific
requirements of the application.

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