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For example: 10101 or (10101) is
2
1
0
3
2
4
= (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
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 formed using 0,1,2,3,4,5,6 and 7. The
base of the octal number system is 8. It is also known as the base-8 system. Each positioning
number represents the power of base 8. The place value of the digits according to position and
weight is as follows:
Position 2 1 0 -1 -2
.
Weights 8 2 8 1 8 0 8 -1 8 -2
For example: (1763) 8
3
= (1 x 8 ) + (7 x 8 ) + (6 x 8 ) + (3 x 8 )
0
1
2
= (1 x 512) + (7 x 64) + (6 x 8) + (3 x 1)
= 512 + 448 + 48 + 3
= 1011 or (1011) 10
HEXADECIMAL NUMBER SYSTEM
A number system made up of sixteen symbols, 0 to 9, and A to F is known as the hexadecimal
number system. When the hexadecimal number system is used, every number is formed using
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E and F, where A = 10, B = 11, C = 12, D = 13, E = 14, and F = 15.
The base of the hexadecimal number system is 16. It is also known as the base-16 system. Each
position represents a power of base 16. The place value of the digits according to position and
weight is as follows:
Position 2 1 0 . -1 -2
Weights 16 2 16 1 16 0 16 -1 16 -2
For Example: (2AF) 16
1
0
= (2 x 16 ) + (A x 16 ) + (F x 16 )
2
= (2 x 256) + (10 x 16) + (15 x 1)
= 512 + 160 + 15
= 687
The hexadecimal number system has made the representation of large values easy. The
hexadecimal numbers are used to represent colours on a webpage, that's why programmers
now prefer hexadecimal numbers.
10 Trackpad (V2.1)-VII

