Binary is a number system that uses only two digits — 0 and 1. Every piece of data inside a computer is ultimately stored and processed as binary digits called bits.
Each column in a binary number represents a power of 2. To convert binary to decimal, add up the column values wherever there is a 1.
Computers are built from transistors — tiny electronic switches with two states: on and off. Binary maps directly on to this: 1 means on, 0 means off. Two states make circuits simpler, more reliable, and far cheaper to manufacture than any system with more distinct values.
Everything a computer does — adding numbers, displaying text, playing a sound — comes down to manipulating on/off states at extraordinary speed.
A single binary digit is a bit. Eight bits make a byte. A byte can represent 256 values (0–255) — enough for one character of text or one pixel of a simple image.
1 kilobyte = 1,024 bytes. 1 megabyte = 1,024 KB. 1 gigabyte = 1,024 MB. These units appear in exam questions about file sizes and storage.
The three systems you need for GCSE are decimal (base 10), binary (base 2), and hexadecimal (base 16).
To convert decimal to binary: find the largest power of 2 that fits, put a 1, subtract, and repeat for each remaining column.
Memorise these 8 values — write them first in every binary question.
Hex uses sixteen symbols: 0–9 then A (10), B (11), C (12), D (13), E (14), F (15). One hex digit represents exactly four binary bits, so long binary strings become much shorter. Web colours use hex — the Miss ICT cyan is #4da9c9.
Group bits into nibbles (groups of 4) from the right. Convert each nibble separately.
Binary: 1010 1111 Nibble1: 1010 = A (=10) Nibble2: 1111 = F (=15) Result: AF
Multiply each hex digit by its place value (powers of 16 from right).
Hex: 3F 3 × 16¹ = 48 F × 16⁰ = 15 Decimal: 63
Binary addition has four rules. Carries happen at 2 rather than 10:
0 + 0 = 0 0 + 1 = 1 1 + 0 = 1 1 + 1 = 10 (write 0, carry 1) 1 + 1 + 1 = 11 (write 1, carry 1)
Add 01101010 and 00110101:
0110 1010 + 0011 0101 ---------- 1001 1111 (= 159)
If the result needs more bits than are available, an overflow error occurs. The leading bit is lost, giving a completely wrong answer. This is a common exam question — you need to spot when it happens and explain why.
Binary questions become much easier when you write the column headers out first before doing anything else.
Always write 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 before you start. Having them visible removes one source of error.
Find the largest power of 2 that fits the number. Mark a 1. Subtract. Repeat. This method never fails.
Convert your binary answer back to decimal to verify. Takes 30 seconds and catches most mistakes.
Binary and data representation appear in almost every GCSE Computer Science paper. Miss ICT sessions focus on the exact methods that get marks — not vague explanations.
For 8-bit binary: 1, 2, 4, 8, 16, 32, 64, 128. Writing them at the top of your answer is fine in the exam.
255 — that is 11111111 in binary or FF in hex. The formula is 2ⁿ − 1 where n is the number of bits.
Yes, constantly. Memory addresses, colour codes, MAC addresses, error codes, and assembly language all use hex because it is far more compact than writing binary.
Both are just different ways of writing numbers. Binary uses base 2, hex uses base 16. Computers store everything in binary — hex is a shorthand humans use to read and write binary values more easily.
Searching, sorting, pseudocode, and trace tables — step by step
Structured practice questions with worked answers
Quick reference card for all major GCSE algorithm types
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