Page 42 - Computer Science V2.0 Class 11

Table 2.5: Decimal and Binary equivalent of Octal Digits.
Decimal Binary representation
Octal digit
representation (3 bits)
0 0 000
1 1 001
2 2 010

3 3 011
4 4 100
5 5 101
6 6 110
7 7 111

The octal number system is also a positional number system. Therefore, each octal digit in an octal number is expressed
as the sum of products of its digits' place values and their face values symbol value. For fractional numbers, the values
of digits on the left side of the radix point (octal point) are expressed as positive powers of eight, while values of digits
on the right side of the radix point are represented as negative powers of eight.

Table 2.6 shows the digit's place value, face value, and value represented by an octal number (307.24) .
8
Table 2.6: Digit's place value, face value, value represented by (307.24) .
8
1
0
-1
2
-2
1
Digit's place value 8 (=64) 8 (=8) 8 (=1) 8 (= ) 8 (= 1 )
8 64
Octal digit 3 0 7 . 2 4
Face value 3 0 7 . 2 4
Value represented 3 × 8 2 0 × 8 1 7 × 8 0 2 × 8 -1 4 × 8 -2
by digit
The decimal value of (307.24) can be calculated as follows:
8
(307.24) 8
-1
2
1
0
=3 × 8 + 0 × 8 + 7 × 8 + 2 × 8 + 4 × 8 -2
=3 × 64 + 0 × 8 + 7 × 1 + 0.25 + 0.0625
=192 + 7 + 0.25 + 0.0625
=199.3125

2.4 Hexadecimal Number System (Base-16)

The hexadecimal number system (also called the base 16 number system) comprises sixteen distinct digits: 0, 1, 2, 3,
4, 5, 6, 7, 8, 9, A, B, C, D, E, and F. While digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 in the hexadecimal system have the same
meaning as the respective digits in the decimal system, the symbols A, B, C, D, E, and F denote the numbers ten, eleven,
twelve, thirteen, fourteen, and fifteen, respectively. Hexadecimal numbers and digits are also called hex numbers and
hex digits, respectively. The hexadecimal number system is also a positional number system. Examples of hexadecimal
numbers are (AB8.6F) , (DAF) , and (D9F.B6C) . Like the octal number system, the hexadecimal number system also
16 16 16
provides a compact representation of binary numbers. A sequence of four bits can take a value from (0000) to (1111) .
2 2
In the hexadecimal system (0000) and (1111) , are expressed as (0) and (F) , respectively. So, a hex digit can be
2 2 16 16
used to represent a sequence of four binary digits (or four bits). Table 2.7 below shows the decimal, octal, and binary
equivalent of each hexadecimal digit.

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