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