Page 8 - Digital Electronics by harish

Symbols used: 0 and 1
Base (or radix, or weight): 2
1
2
-3
3
-1
-2
0
Place value: ….. 2 , 2 , 2 , 2 . 2 , 2 , 2 …..

Octal number system

Octal numbers are used to represent binary numbers. It has eight symbols: 0, 1, 2, 3, 4, 5, 6
and 7. The base (or radix, or weight) of the octal number system is 8. The place value of each
position is given below:

-1
-2
-3
2
1
0
3
8 8 8 8 . 8 8 8
512 64 8 1 . 0.125 0.015625 0.001953125

Example:

0
1
72.2 = 7 x 8 + 2 x 8 + 2 x 8 -1
= 7 x 8 + 2 x 1 + 2 x 0.125
= 58.25 (in decimal)

Symbols used: 0, 1, 2, 3, 4, 5, 6 and 7
Base (or radix, or weight): 8
3
2
1
0
-1
-2
-3
Place value: ….. 8 , 8 , 8 , 8 . 8 , 8 , 8 …..

Hexadecimal number system

Hexadecimal numbers are used to represent binary numbers. It has sixteen symbols: 0, 1, 2, 3,
4, 5, 6, 7, 8, 9, A, B, C, E and F. The base (or radix, or weight) of the hexadecimal number
system is 16. Here the decimal number for „A‟ is 10, „B‟ is 11, „C‟ is 12, „D‟ is 13, „E‟ is 14
and „F‟ is 15. The place value of each position is given below:

-1
1
-3
-2
2
0
3
16 16 16 16 . 16 16 16
4096 256 16 1 . 0.0625 0.00390625 0.000244140625

Example:

0
1
3C.A = 3 x 16 + 12 x 16 + 10 x 16 -1
= 3 x 16 + 12 x 1 + 10 x 0.0625
= 60.625 (in decimal)

Symbols used: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E and F
Base (or radix, or weight): 16
-2
-3
3
2
1
0
-1
Place value: ….. 16 , 16 , 16 , 16 . 16 , 16 , 16 …..

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