Cambridge A-Level Computer Science (9618) · lesson 1 of 15 · 30 min
Number Systems Review and Extension
At A-Level, you extend IGCSE number system knowledge to include octal (base-8) and deeper hexadecimal work, and you must be fluent in converting between all bases.
Octal Conversion
Octal uses groups of 3 binary bits (since 2³ = 8). To convert binary → octal, split into groups of 3 from the right:
Convert binary 110101011 to octal
Group: 110 | 101 | 011
110 = 6, 101 = 5, 011 = 3
= 653 (octal)
Converting Between Any Bases
The universal method: convert to denary first, then to the target base. Or use the shortcut: binary ↔ hex (groups of 4), binary ↔ octal (groups of 3).
Convert hex 2AF to denary
2 × 16² + A(10) × 16¹ + F(15) × 16⁰
= 2 × 256 + 10 × 16 + 15 × 1
= 512 + 160 + 15 = 687
How many binary bits correspond to one octal digit?
- 2
- 3
- 4
- 8
Answer: 3
2³ = 8, so one octal digit represents exactly 3 binary bits.
What is hex FF in denary?
- 240
- 255
- 256
- 250
Answer: 255
15×16 + 15 = 240 + 15 = 255.
Convert denary 100 to hexadecimal.
- 64
- 6A
- 6E
- 60
Answer: 64
100 ÷ 16 = 6 remainder 4 → 64 hex.
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