Hexadecimal: Conversions Between Binary, Denary, and Hex

Hexadecimal (base-16, often shortened to "hex") is the third number system you need to know for OCR J277 Section 2.6. Hexadecimal is widely used in computing because it provides a compact, human-readable representation of binary data.

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Why Hexadecimal?

Binary numbers are long and hard for humans to read. Hexadecimal solves this problem:

Binary (8 bits)	Denary	Hexadecimal
11111111	255	FF
10101010	170	AA
00000000	0	00

Hex is shorter and easier to read than binary, while still mapping directly to binary (each hex digit = exactly 4 bits). This is why hex is used for:

Use	Example
Colour codes	#FF5733 (red, green, blue values)
MAC addresses	4A:2B:7C:DE:01:FF
Memory addresses	0x7FFF0000
Error codes	0x80070005
HTML/CSS colours	color: #00FF00 (green)

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Hexadecimal Digits

Hex uses 16 digits. Since we only have 10 numeral symbols (0-9), the letters A-F represent values 10-15:

Hex digit	Denary value	Binary (4 bits)
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

OCR Exam Tip: You should memorise this table. In the exam, you can quickly write the hex-to-binary lookup in the margin to help with conversions.

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Converting Binary to Hexadecimal

1. Split the binary number into groups of 4 bits from the right
2. Convert each group to a hex digit using the table above

Example: Convert 10110111 to hex

Split: 1011 | 0111

• 1011 = B
• 0111 = 7

Answer: B7

Example: Convert 11111010 to hex