Page 43 - Computer Science V2.0 Class 11

Table 2.7: Decimal, Octal and Binary (4 bits) equivalents of Hexadecimal digits

Hexadecimal 1 Decimal Octal Binary representation
Digit representation representation (4 bits)

0 0 0 0000
1 1 1 0001
2 2 2 0010
3 3 3 0011
4 4 4 0100
5 5 5 0101
6 6 6 0110
7 7 7 0111

8 8 10 1000
9 9 11 1001
A 10 12 1010
B 11 13 1011
C 12 14 1100
D 13 15 1101
E 14 16 1110
F 15 17 1111

Consider the number (2AE.C8) . Its symbol value and positional value are illustrated in Table 2.8.
16
Table 2.8: Face value and place value of digits of an octal number
1
0
-1
2
-2
Digit's place value 16 (=256) 16 (=16) 16 (=1) 16 (= 1 ) 16 (= 1 )
16 256
hex digit 2 A E . C 8
Face value 2 10 14 . 12 8
Value represented by digit 2 × 16 2 10 × 16 1 14 × 16 0 12 × 16 -1 8 × 16 -2
The computation of decimal value of (2AE.C8) is shown below:
16
(2AE.C8) 16
2
-1
0
1
= 2 × 16 + A × 16 + E × 16 + C × 16 + 8 × 16 -2
= 2 × 256 + 10 × 16 + 14 + 0.75 + 0.03125
= 512 + 160 + 14 + 0.75 + 0.03125
= 686.78125
Application of Hexadecimal Numbers
We describe three important uses of hexadecimal numbers:
● Hexadecimal numbers have been used for developing software for microprocessor kits as it is easy to describe the
addresses and names of registers using hexadecimal notation.
● Hexadecimal numbers find use in describing the network addresses (to be discussed in a later chapter).
● Hexadecimal numbers are also used to represent colour codes in digital form. Each colour comprises three primary
colours: red, green and blue (also referred to as RGB). A number between 0 and 255 expresses the intensity of each
colour, often expressed as a two-digit hexadecimal number between 00 and FF. Thus, if red and green colours are
present in full intensity and the blue colour is absent, the intensity triplet (R, G, B) would be expressed as (FF, FF, 00)
in the hexadecimal system or as (255, 255, 0) in the decimal system.

Number Systems and Encoding Schemes 29