Hexadecimal system

The base 16 or hexadecimal system is a natural way to rep-resent the binary data stored in a computer. It is more com-pact than binary because four binary digits can be replaced by a single “hex” digit.

The following table gives the corresponding decimal, binary, and hex values from 0 to 15:

Decimal Binary Hex

0 0                 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

10 1010         A

11 1011                B

12 1100         C

13 1101                D

14 1110                E

15 1111                F

Note that decimal and hex digits are the same from 0 to 9, but hex uses the letters A–F to represent the digits cor-responding to decimal 10–15. The system extends to higher numbers using increasing powers of 16, just as decimal uses powers of 10: For example, hex FF represents binary 11111111 or decimal 255. Many of the apparently arbitrary numbers encountered in programming can be better under-stood if one realizes that they correspond to convenient groupings of bits: FF is eight bits, sufficient to hold a single character (see characters and strings). In low-level pro-gramming memory addresses are also usually given in hex (see assembler).