Hexadecimal

Hexadecimal (or hex) is a base 16 system used to simplify how binary is represented. A hex digit can be any of the following 16 digits: 0 1 2 3 4 5 6 7 8 9 A B C D E F.

Each hex digit reflects a 4-bit binary sequence.

This means an 8-bit binary number can be written using only two different hex digits – one hex digit for each nibble (or group of 4-bits). It is much easier to write numbers as hex than to write them as binary numbers.

For example:

• 11010100 in binary would be D4 in hex
• FFFF3 in hex would be 11111111111111110011 in binary

This table shows each hex digit with the equivalent values in binary and denary.

Denary	Binary	Hexadecimal
0	0000	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

Hex codes are used in many areas of computing to simplify binary codes. It is important to note that computers do not use hexadecimal – it is used by humans to shorten binary to a more easily understandable form. Hexadecimal is translated into binary for computer use. Some examples of where hex is used include:

• Colour references
• Assembly language programs
• Error messages

To represent the denary number 12 in a computer system, you could use binary 1100 or hex value C.

To convert a 4-bit binary number to hex:

Binary	Denary	Hex
1100	(1×8) + (1×4) + (0x2) + (0x1) = 12	C

 

A byte is made of eight binary digits. To convert an 8-bit binary number to hex, separate it into two nibbles or two half-bytes.

Binary	Denary	Hex
1011 1001	11 and 9	B9

Separate the hex digits to find each equivalent in binary, and then piece them back together.

What is the denary value of hex value 2D?

Separate the hex digits into 2 and D and find the equivalent binary numbers (2 = 0010; D = 1101).

Piece them together to get 00101101 (0x128 + 0x64 + 1×32 + 0x16 + 1×8 + 1×4 + 0x2 + 1×1 = 45 in denary)

The below worksheet shows some of the conversion that were done during the SKE.

Hexadecimal Worksheet