# Return to the numbers pages | Decimal Numbers | Binary Numbers | Hexadecimal Numbers | Octal Numbers | BCD Number | Negative Numbers | Number Conversions

Hexadecimal, simply referred to as Hex, is a base-16 number system.

Most modern day PLC/PAC's use the hexadecimal number system some where within their architecture. Some PLC/PAC require that some instruction parameters be entered in Hex.

Base-16 numbers can be written in two formats:

2416  or   24h
in ControlLogix: 16#24

Base-16 also means that there are 16 valid numbers. Starting with zero they are:

0, 1, 2, 3, 4, 5, 6, 7, 8, 9
A, B, C, D, E, F

Where:

A = 10, B = 11, C = 12, D = 13, E = 14, F = 15

Question to Ponder and Research
Why the switch to letters? Why not simply use the numbers 10 through 15?
How many bits of binary does it take to represent all 16 digits of a hex number?
The answer is that it takes 4-bits of binary to represent any hex digit. The following table shows the hex digits and the corrisponding 4-bit binary number.
Hex Number 4-bit Binary
0 0000
1 0001
2 0010
3 0011
4 0100
5 0101
6 0110
7 0111
8 1000
9 1001
A (10) 1010
B (11) 1011
C (12) 1100
D (13) 1101
E (14) 1110
F (15) 1111

Each digit in a hexadecimal number has a weight Value. The weight of a hex digit is the base raised to the power of the digit position. The figure below depicts an example. 