Hexadecimal Representation

Hexadecimal (hex) is a base-16 number system. Where binary uses two digits (0–1) and denary uses ten (0–9), hexadecimal uses sixteen: 0–9 followed by A–F to represent the values ten through fifteen in a single character.

Computers store everything in binary, but long binary strings — for example, a 32-bit memory address — are difficult to read and prone to transcription error. Hexadecimal solves this by providing a compact notation: every 4 binary bits map exactly to a single hex digit, making the conversion lossless.

Where hex appears	Example
Web colour codes	#FF5733
Memory addresses	0x1A2F
MAC addresses	A8:5E:45:6B:3C:71
Error codes	0x000000ED

Hex is used in computing not because it is intuitive, but because 4 bits = 1 hex digit. Binary-to-hex conversion is exact, with no rounding or information loss.

The sixteen hex digits and their denary equivalents must be memorised. Digits 0–9 behave identically to denary; A–F replace the two-digit denary values 10–15 with a single character.

Hex	Denary	4-bit binary
0	0	0000
1	1	0001
2	2	0010
3	3	0011
4	4	0100
5	5	0101
6	6	0110
7	7	0111
8	8	1000
9	9	1001
A	10	1010
B	11	1011
C	12	1100
D	13	1101
E	14	1110
F	15	1111

The most common error here is treating A as 11 rather than 10. A is the first letter after the digits, and 10 is the first value after 9. Each subsequent letter adds one: B = 11, C = 12, D = 13, E = 14, F = 15.

Each hex digit represents a power of 16, starting from $16^0=1$ at the rightmost position. Multiply each digit by its place value, substituting the denary equivalent for any letter, then sum the results.

For a 2-digit hex number:

Position	Place value
Left digit	$16^1=16$
Right digit	$16^0=1$

Worked example 1 — convert 2A to denary:

• 2 × 16 = 32
• A (= 10) × 1 = 10
• Total: 32 + 10 = 42

Worked example 2 — convert B7 to denary:

• B (= 11) × 16 = 176
• 7 × 1 = 7
• Total: 176 + 7 = 183

Substitute the denary value for each letter before multiplying. Multiplying "A" directly is a common source of arithmetic errors.