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Binary Number System
A number system made up of only two digits: 0 and 1, is known as the binary number system.
In the binary number system, every number is represented using the digits 0 and 1. The word
binary comes from ‘Bi’ meaning two that’s why the base of the binary number is 2. It is also
known as the base-2 system.
Name Size (bits) Examples
Bit 1 0 or 1
Nibble 4 1010, 1001
Byte 8 10101010, 11110011
Word 16 1010101010101010, 1111000011110011
Formation of Binary numbers
Each digit or bit in a binary number system can either be 0 or 1. A combination of binary digits
may be used to represent different quantities like 1001. The positional value of each digit in a
binary number is twice the place value or face value of the digit on its right side. The weight of
each position is a power of 2. The place value of the digits according to position and weight is
as follows:
Position 3 2 1 0 –1 –2
.
Weight 2 3 2 2 2 1 2 0 2 –1 2 –2
For example: 10101 or (10101) is
2
1
4
3
0
2
= (1 × 2 ) + (0 × 2 ) + (1 × 2 ) + (0 × 2 ) + (1 × 2 )
= (1 × 16) + (0 × 8) + (1 × 4) + (0 × 2) + (1 × 1)
= (21)
10
Info Byte
If the last digit of a binary number is 1, the number is odd; if it is 0, the number is even.
Octal Number System
A number system made up of eight digits from 0 to 7, is known as the octal number system.
When the octal number system is used, every number is represented using the digits 0 to 7. The
base of the octal number system is 8. It is also known as the base-8 system. In the octal number
system, each digit’s position represents a power of 8.
The place value of the digits according to position and weight is as follows:
Position 3 2 1 –1 –2
.
Weight 8 2 8 1 8 0 8 –1 8 –2
For example: (1763)
8
3
0
1
2
= (1 × 8 ) + (7 × 8 ) + (6 × 8 ) + (3 × 8 )
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Number System

