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The digit 7 in the number 724 is the most significant digit and 4 is the least significant digit.
The table shows the positional weight of decimal number (724) .
10
Hundreds Ten Units
Weights 10 2 10 1 10 0
Real Value of each digit 7 × 10 2 2 × 10 1 4 × 10 0
Result 700 20 4
For Example: (3698) 10
8 signifies 8 x 10 = 8
0
1
9 signifies 9 x 10 = 90
2
6 signifies 6 x 10 = 600
3
3 signifies 3 x 10 = 3000
Upon adding them = 3000 + 600 + 90 + 8 = 3698
BINARY NUMBER SYSTEM
A number system made up of only two digits: 0 and 1, is known as the binary number system.
When the binary number system is used, every number is formed using only 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.
Formation of Binary Numbers
Each digit or bit in a binary number system can 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
•
Weights 2 3 2 2 2 1 2 0 2 –1 2 –2
For example: 10101 or (10101) is
2
1
0
4
3
2
= (1 x 2 ) + (0x 2 ) + (1x 2 ) + (0x 2 ) + (1x 2 )
= (1 x 16) + (0 x 8) + (1 x 4) + (0 x 2) + (1 x 1)
= (21) 10
Number System 9

