Hexadecimal Number System
The Hexadecimal number system has a radix of 16 and uses 16 symbols, namely 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A ,B, C, D, E and F. The symbols A, B, C , D, E and F represent the decimal 10, 11, 12, 13, 14 and 15 respectively. Each significant position in a hexadecimal number has a positional weight. The least significant position has a weight of 160, i.e.1; the higher significant positions are given weights in the ascending powers of sixteen, i.e. 161, 162, 163, etc. respectively. The hexadecimal equivalent of a decimal number can be obtained by dividing the given number by 16 repeatedly, until a quotient of 0 is obtained. The following example illustrates how the hexadecimal equivalent of a given decimal is obtained.
Hexadecimal to Binary Conversion
Conversion from hexadecimal to binary and vice versa can be easily carried out. For arriving at the binary equivalent of a hexadecimal number, each significant digit in the given number is replaced by its 4-bit binary equivalent.
For example,
(2D5)16= 2 D 5
0010 1101 0101
Thus, (2D5)16 =(001011010101)2. The reverse procedure is used for converting a binary number to an hexadecimal, i.e. starting from the least significant bit, each group of 4-bits is replaced by its decimal equivalents.
For example,
(11110110101)2 = 0111 1011 0101
7 B 5
Thus,
(11110110101)2=(7B5)16
Hexadecimal to Octal Conversion
Conversion from hexadecimal to octal and vice versa is sometimes required. To convert a hexadecimal number to octal, the following steps can be applied.
1. Convert the given hexadecimal number to its binary equivalent.
2. Form groups of 3 bits, starting from the LSB (least significant digit).
3. Write the equivalent octal number for each group of 3 bits.