Number Bases for GCSE Computer Science — Complete Guide

Number bases are a core topic in GCSE Computer Science — and one that trips up many students because the logic feels unfamiliar at first. This guide covers binary, hexadecimal, octal, and decimal in plain English: what each base means, how to convert between them, and how to check your answers. The free converter at the end of each section lets you verify your work instantly.

What Is a Number Base?

A number base (or radix) determines how many distinct symbols a number system uses for each digit position. When that count is reached, you carry over into the next position.

Decimal (everyday numbers) is base 10 — it uses ten symbols (0-9), and you carry over when you hit 10. Binary is base 2 — it uses two symbols (0 and 1), and carries over at 2. Hexadecimal is base 16 — it uses sixteen symbols (0-9 and A-F), and carries over at 16.

Base	Name	Symbols	Count Before Carry
2	Binary	0, 1	2
8	Octal	0–7	8
10	Decimal	0–9	10
16	Hexadecimal	0–9, A–F	16

Binary — How Computers Think

Binary is the foundation of all computing. Every piece of data — images, text, numbers, programs — is ultimately stored and processed as sequences of 0s and 1s. Each 0 or 1 is one bit. Eight bits make a byte.

Reading binary place values: Binary uses powers of 2. Reading from right to left: 1, 2, 4, 8, 16, 32, 64, 128.

Example: Convert binary 10110 to decimal

• 0 × 1 = 0
• 1 × 2 = 2
• 1 × 4 = 4
• 0 × 8 = 0
• 1 × 16 = 16
• Total: 0 + 2 + 4 + 0 + 16 = 22

Converting decimal to binary: Divide repeatedly by 2, reading remainders from bottom to top. 22 ÷ 2 = 11 R0 → 11 ÷ 2 = 5 R1 → 5 ÷ 2 = 2 R1 → 2 ÷ 2 = 1 R0 → 1 ÷ 2 = 0 R1. Reading up: 10110.

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Hexadecimal — The Programmer's Shorthand

Hexadecimal exists because binary strings get long and unreadable fast. A 32-bit binary value is 32 characters. The same value in hex is 8 characters. Hex is a compact encoding of binary that programmers use for memory addresses, color codes, and error codes.

The key fact: 4 binary bits = 1 hex digit. Every hex digit maps to exactly a 4-bit binary group:

• 0 = 0000, 1 = 0001, 2 = 0010, 3 = 0011, 4 = 0100, 5 = 0101
• 6 = 0110, 7 = 0111, 8 = 1000, 9 = 1001, A = 1010, B = 1011
• C = 1100, D = 1101, E = 1110, F = 1111

Converting hex to decimal: Use place values that are powers of 16 (1, 16, 256, 4096...). Hex 2F = (2 × 16) + (15 × 1) = 32 + 15 = 47.

Octal — File Permissions and Legacy Systems

Octal uses 8 symbols (0-7). Place values are powers of 8 (1, 8, 64, 512...). Octal conversion uses the same divide-and-remainder method as binary, but dividing by 8 instead of 2.

Converting decimal 75 to octal:

• 75 ÷ 8 = 9 remainder 3
• 9 ÷ 8 = 1 remainder 1
• 1 ÷ 8 = 0 remainder 1
• Read up: 113 (octal)

Octal is commonly tested in GCSE exams even though it is rarely used in modern programming (except Unix file permissions, where chmod values like 755 and 644 are octal).

Exam-Ready: Converting Between Bases

For the exam, you need to move confidently between any two bases. The general strategy:

• To/from decimal: Use divide-and-remainder (decimal to other) or place-value sum (other to decimal)
• Binary ↔ Hex shortcut: Group 4 binary bits = 1 hex digit (no need to go through decimal)
• Binary ↔ Octal shortcut: Group 3 binary bits = 1 octal digit

Practice by trying a conversion manually, then checking it in the Number Base Converter. The tool shows all four bases simultaneously, so you can cross-check your working. Use the practice problems page to build speed before your exam.

Frequently Asked Questions

What number bases do I need for GCSE Computer Science?

The main GCSE specifications (AQA, OCR, Edexcel) cover binary (base 2), hexadecimal (base 16), and denary/decimal (base 10). Some specifications also include octal (base 8). You need to convert between all of these both manually and with tools.

Is octal on the GCSE Computer Science exam?

It depends on the exam board. AQA GCSE Computer Science does not typically include octal, but OCR may. Check your specification document for your specific exam board to confirm what is required.

How do I remember the hex digits A through F?

The values A through F represent decimal 10 through 15. One approach: memorize A=10, then count up. Another: learn the 4-bit binary patterns (A=1010, B=1011, C=1100, D=1101, E=1110, F=1111) — each increases by one in binary.