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

 

Hexadecimal Number Chart:

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

Decimal to Hexadecimal Conversion

Decimal to Hexadecimal Conversion


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

Hexadecimal to Decimal Conversion

Hexadecimal to Decimal Conversion




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