Hexadecimal
Number System

Base-16 · Hex ↔ Binary · Hex ↔ Denary · Uses in Computing

CSZoneCambridge IGCSE Computer Science 0478

Hexadecimal Basics

Base-16: 0–9 and A–F

Denary	0	1	...	9	10	11	12	13	14	15
Hex	0	1	...	9	A	B	C	D	E	F

Hexadecimal uses 16 symbols: digits 0–9 and letters A–F

One hex digit = exactly 4 binary bits (a nibble) — making conversion easy

Used in: colour codes (#FF5733), MAC addresses, memory addresses, error codes

Hex ↔ Binary Conversion

Group into Nibbles

Binary → Hex: group 4 bits from right
1011 1110 = B E = BE

Hex → Binary: expand each digit to 4 bits
A F = 1010 1111 = 10101111

More examples:
0101 0100 = 5 4 = 54₁₆
C 9 = 1100 1001 = 11001001₂

Always pad to 4 bits per nibble: hex 3 = binary 0011 (not 11)

Hex ↔ Denary Conversion

Using Place Values

Hex place values: 256 (16²) | 16 (16¹) | 1 (16⁰)

Convert 2B₁₆ to denary:
2 × 16 + 11 × 1 = 32 + 11 = 43

Convert 154 to hex:
154 ÷ 16 = 9 remainder 10 → 9A₁₆
Check: 9 × 16 + 10 = 144 + 10 = 154 ✓

Hex → denary: multiply each digit by its place value (16⁰, 16¹, 16²...)

Denary → hex: divide by 16 repeatedly; remainders give hex digits

Exam Practice

Have a go at this question

Cambridge IGCSE 0478 style

Convert the hexadecimal number 3F to (a) binary and (b) denary. Show your working.

3 marks

(a) 3 = 0011, F = 1111 → 00111111 [1]. (b) 3×16 + 15×1 = 48 + 15 = 63 [2].

Key Takeaways

What to Remember

Hex is base-16: digits 0–9 then A (10), B (11), C (12), D (13), E (14), F (15)

1 hex digit = 4 binary bits; split/group at nibble boundaries

Hex → denary: multiply digits by powers of 16 and sum

Used for memory addresses, colour codes (#RRGGBB), error codes — compact and readable