Hexadecimal Number System
beginner20 minLearning objectives
- Explain the purpose of hexadecimal
- Convert between hexadecimal, binary and denary
- Identify practical computing applications of hexadecimal
Learn
AQA 4.5.3 — Hexadecimal
Binary numbers get long and hard for humans to read. Hexadecimal (base 16, digits 0–9 then A–F) groups binary digits into 4s — each hex digit represents exactly one nibble — making it a compact, human-friendly shorthand for binary that's trivial to convert.
1001 1100 → split into nibbles 1001 and 1100 → 9 and C → 9C in hexadecimal.
Converting hex to denary
9C = (9 × 16) + (12 × 16⁰) = 144 + 12 = 156 (matching the binary conversion example from the previous lesson — 10011100 = 9C = 156, all the same value in three representations).
Real uses of hexadecimal
- HTML colour codes:
#FF5733— three pairs of hex digits for red, green, blue. - Memory addresses in debuggers and low-level programming.
- MAC addresses:
00:1A:2B:3C:4D:5E.
Common mistake
A single hex digit represents exactly 4 binary digits (a nibble), not one binary digit or an arbitrary number — students sometimes forget to pad a nibble with leading zeros before converting (e.g. binary 0011 for hex digit 3 needs all 4 bits, not just 11), which throws off the grouping for every digit after it.
Try it yourself
Investigate the HTML colour code #4F46E5 (used on this platform) — convert each pair of hex digits to denary to find the red, green and blue values, then to binary.