Hexadecimal number system:


Hexadecimal is a number system with a base of 16, usually used in computing. There are 16 symbols or digits in hexadecimal number system. The first 10 digits are like decimal number system - 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 and the remaining six digits are the symbols A, B, C, D, E, F, representing decimal values 10, 11, 12, 13, 14, and 15, respectively. Each place in a number increases in value of 16 going from right to left.

Example:

1FF₁₆ = 1*16 + F* 16 + F*16⁰
= 1*256 + 15*16 + 15*1
= 256 + 240 + 15
= 511

Hexadecimal numbers are often preferred by programmers writing in low language because they are more easily converted to the computer’s internal binary code than the decimal numbers. Hexadecimal numbers are more compact than binary numbers and therefore more easily keyed, checked and memorized.
Since there are only 16 digits in hexadecimal number system, 4 bits ( 2⁴= 16) are sufficient to represent any hexadecimal number in binary.

The table given displays the Binary and Decimal equivalents of some hexadecimal numbers.

Hexadecimal Binary Decimal
0 0000 0
1 0001 1
2 0010 2
3 0011 3
4 0100 4
5 0101 5
6 0110 6
7 0111 7
8 1000 8
9 1001 9
A 1010 10
B 1011 11
C 1100 12
D 1101 13
E 1110 14
F 1111 15

The Hexadecimal number 4B3A translates to the following Binary number:

4 B 3 A
0100 1011 0011 1010

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