AQA 8525 · Section 3.3 · 3.3.2

Converting
Between Bases

Binary↔Denary · Binary↔Hex · Denary↔Hex

CSZoneAQA GCSE Computer Science 8525

Binary → Denary

Write out place values, add the 1s

Convert 1011 0110 to denary:

1

128

0

64

1

32

1

16

0

8

1

4

1

2

0

1

128 + 32 + 16 + 4 + 2 = 182

Denary → Binary

Subtract place values from largest

Convert 109 to binary:

109 ≥ 128? No → 0
109 ≥ 64? Yes → 1 (109 - 64 = 45)
45 ≥ 32? Yes → 1 (45 - 32 = 13)
13 ≥ 16? No → 0
13 ≥ 8? Yes → 1 (13 - 8 = 5)
5 ≥ 4? Yes → 1 (5 - 4 = 1)
1 ≥ 2? No → 0
1 ≥ 1? Yes → 1

Result: 01101101

Binary ↔ Hexadecimal

Group into nibbles (4 bits)

BINARY → HEX

10110110
Split: 1011 | 0110
1011 = 11 = B
0110 = 6
Answer: B6

HEX → BINARY

2F
2 = 0010
F = 15 = 1111
Answer: 0010 1111

Key:Each hex digit = exactly 4 binary bits. No intermediate denary conversion needed!

Exam Practice

Have a go at this question

AQA-style question

(a) Convert denary 75 to binary.
(b) Convert binary 11001010 to hexadecimal.

4 marks

(a) 64+8+2+1 = 75 → 01001011 [2]
(b) Split: 1100 | 1010 → 12=C, 10=A → CA [2]

Key Takeaways

What to Remember

Binary → Denary: write place values, add the 1s

Denary → Binary: subtract largest fitting place value, repeat

Binary ↔ Hex: group into nibbles of 4 bits — direct conversion

Place values: 128, 64, 32, 16, 8, 4, 2, 1 — memorise these!