# Hexadecimal Number system and Their Conversion

The number with base 16 is called hexadecimal number. It is denoted by H. It has 16 symbols starting from 0 to 15. The following table shows relationship between hexadecimal and binary numbers.

The 4-bit format of binary is used for hexadecimal to binary conversion.

Weighted value:

 $16^ 5$ $16^ 4$ $16^ 3$ $16^ 2$ $16^1$ $16^0$ 1048576 65536 4096 256 16 1

 Decimal Octal Hexadecimal Binary 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 1000 9 9 1001 10 A 1010 11 B 1011 12 C 1100 13 D 1101 14 E 1110 15 F 1111

A big problem with the binary system is verbosity. When dealing with large values, binary numbers too unwieldy. The hexadecimal number system solves these problems.

Hexadecimal numbers offer the two features:

(a) Hexadecimal numbers are very compact.

(b) It is easy to convert into binary and vice Versa.

(a) Binary to Hexadecimal Conversion: The binary numbers are broken into sections of 4-bit digits from LSB to MSB and its hexadecimal equivalent is assigned for each section.

Example:

Q. Convert (11 10 11)2 into base 16.

Solution:

(11 10 11)2 = 0011 1011= (3B)16

Hints: Add two 00 left to binary and make group of each 4 digits.

0011 =3 and 1011=B

(b) Hexadecimal to Binary Conversion: Binary equivalent of each hexadecimal digit is written in the 4-bit format or section.

(c) Decimal to Hexadecimal conversion: The decimal number is repetitively divided by 16 and remainders are collected to represent hexadecimal numbers.

Q. Convert following in hexadecimal number: (1047)10 = (417)16

(d) Hexadecimal to Decimal: Each hexadecimal digit is multiplied by weighted positions, and sum of product is equal to decimal value.