2. HOW COMPUTER REPRESENT DATA
• Number system
• Manner of Counting
• Several different number systems
exist
• To Computer everything is a
number
• Alphabets, numbers, punctuation
marks, sound, pictures, computer
instructions
• For example
• “Here are some words.” 2
3. NUMBER SYSTEM
• A term used for a set of different symbols or
digits, which represent a numerical value.
• The number system varies according to their
names, characteristics and utilization.
• When we type some letters or words, the
computer translates them in numbers as
computers can understand only numbers.
3
4. HOW COMPUTER REPRESENT DATA
• Number system
• Manner of Counting
• Several different number systems
exist
• To Computer everything is a
number
• Alphabets, numbers, punctuation
marks, sound, pictures, computer
instructions
• For example
• “Here are some words.” 4
5. 4-COMMONLY USED NUMBER
SYSTEMS
1. Decimal Number System
2. Binary Number System
3. Octal Number System
4. Hexadecimal Number System
5
6. DECIMAL NUMBER SYSTEM
• The most popular and commonly used number system is the
Decimal Number system.
• Supports mathematical and accounting concepts
• Also called as Natural number system, because its natural to
humans.
• Composed of 10 symbols or digits (deci means 10).
• Base of the system shows the total number of digits that
constitute a system.
• Base of decimal system is 10.
0 1 2 3 4 5 6 7 8 9
• 0 is the small and 9 is the highest.
• Each position represents a specific power of the base (10).
6
7. The system is based on the idea of place value.
•Place value:
•Particular digit has the value because of its place or position with
in the series of digits.
•E.g. number 345 is recognized as “ three hundred and fourty five”
because of place value.
•we recognize it as 5 in unit position 5*100
•4 represents 4 tens or 4*101
•3 represents 3 hundreds or 3*102
•Digit(3) carries most weight and is called the most significant bit
while 5 carries the least weight and is called least significant bit.
8. BINARY NUMBER SYSTEM
• Binary number system consists of two
digits
• Switch has two states
• Off represents 0, On is 1
• Latin bi means 2
• Used by computers to count
• Two distinct digits, 0 and 1
• 0 and 1 combine to make numbers
• represent a quantity >1 it uses two (or
more) digits
• Pattern repeats indefinitely
8
9. MOST SIGNIFICANT BIT AND LEAST SIGNIFICANT BITS
• Binary or base 2 system uses place value exactly same way as the decimal
system.
• Place value increases by power of 2.
• The left most binary digit(bit) is called Most significant bit(MSB)
• Right most binary digit(bit) is called Least significant bit(LSB).
MSB:
• The most significant bit (MSB) is the bit in a multiple-bit binary number with the
largest value.
• This is usually the bit farthest to the left, or the bit transmitted first in a
sequence. For example, in the binary number 1000, the MSB is 1, and in the
binary number 0111, the MSB is 0.
LSB:
• The least significant bit or byte (LSB) is usually the one farthest to the right (or
last).
9
10. OCTAL NUMBER SYSTEM
• As the name implies made up of 8 digits or symbols
(octal means eight) representing their unique values
depending upon their positional values.
• 0 1 2 3 4 5 6 7
• The base of the system is 8.
• Each digit or symbol determines its value or
significance in the power of 8.
10
11. HEXA DECIMAL NUMBER SYSTEM
•The hexadecimal number system has 16 digits or symbols.
•Hexa means 6 and deci means 10.
•Sum is 16, hence has the base 16.
•Uses numerical values from 0-9 and alphabets from A-F.
•A-F represents decimal numbers from 10 to 15.
•Required in assembly language programming
11
12. CONVERSIONS
• Computer uses binary notations and binary
codes;
• Arithmetic are converted to binary numbers,
processed and then the result is converted back
to the required number system.
12
Editor's Notes
#10: In computing environments, it is commonly used as a shorter representation of binary numbers by grouping binary digits into threes.
The chmod command in Linux or UNIX uses octal to assign file permissions.
It helps us to create an identity among billions of data in the database. Hexadecimal numbers will lessen up the load of creating smaller id’s than with decimal numbers.
All modern computers use binary for their internal storage. This is due to the ease the hardware can represent binary values (on or off).
However humans have issues dealing with large strings of binary numbers.
For example, the number 128 decimal is 10000000 in binary. Larger numbers get even harder to deal with (for humans). However if binary numbers are grouped in groups of 3, then it is easy to view the numbers in octal. Or groups of 4 make hexadecimal numbers. So 128 decimal is 200 octal or 80 hex. It’s all the same number but the larger bases make it easier for humans to use.
