Hexadecimal

What hexadecimal is

Hexadecimal (hex) is a base-16 number system. Everyday numbers use base 10 (digits 0–9); binary uses base 2 (0 and 1); hex uses sixteen symbols: 0 1 2 3 4 5 6 7 8 9 A B C D E F.

The letters stand for the denary values that are too big for a single digit:

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

Why hex is used

Computers work in binary, but long binary strings are hard for people to read and easy to mis-copy. Hex is a compact, human-friendly shorthand:

• One hex digit = exactly 4 bits (one nibble).
• Two hex digits = 1 byte (8 bits).

So the byte 11111010 becomes just FA — far quicker to read, write and spot errors in. You'll see hex in:

• Colour codes — #FF0000 is red (FF = 255 red, 00 green, 00 blue).
• Memory addresses — e.g. 0x7FFF.
• MAC addresses — e.g. 00:1B:44:11:3A:B7.
• Error/debugging codes and machine code.

Converting between the bases

Binary → Hex

Split the binary into nibbles of 4 bits (from the right), then convert each nibble:

1111 1010
 F    A     →  FA

If the left-hand group has fewer than 4 bits, pad with leading zeros: 101110 → 0010 1110 → 2E.

Hex → Binary

Convert each hex digit into its 4-bit group:

2 D  →  0010 1101

Hex → Denary

Multiply the first digit by 16 and add the second:

2D = (2 × 16) + 13 = 32 + 13 = 45

Denary → Hex

Divide by 16. The whole-number answer is the first digit; the remainder is the second:

45 ÷ 16 = 2 remainder 13  →  2D

Worked example

Convert the byte 11001111 to hex.

1. Split into nibbles: 1100 1111

2. Convert: 1100 = 12 = C, 1111 = 15 = F

3. Answer: CF

Common mistakes

• Forgetting to pad the left nibble with zeros (e.g. writing 101 as 5 from 1 01 instead of 0101).
• Mixing up that A = 10, not 1, and F = 15, not 16.
• Splitting nibbles from the left instead of the right on odd-length binary.

Exam tips

• Memorise the four "letter" values: A=10, B=11, C=12, D=13, E=14, F=15.
• Most hex questions are just two separate nibble conversions joined together — do them one nibble at a time.
• Show the nibble split in your working; you often get a mark for method even if the final digit is wrong.

Key facts to remember

• Hex is base 16; digits 0–9 then A–F.
• 1 hex digit = 4 bits (a nibble); 2 hex digits = 1 byte.
• Used for colour codes, memory/MAC addresses and machine code because it is shorter and less error-prone than binary.