Binary Numbers Explained for KS3 Computing Students

Binary is a base-2 number system that uses only two digits — 0 and 1 — to represent every number, letter, image and sound stored in a computer. At KS3, students learn to convert between binary and decimal, and understand why electronic computers are built on just two states.

Why do computers use binary?

Modern computers are built from billions of tiny electronic switches called transistors. Each transistor is either on (carrying current) or off (not carrying current). On maps to 1; off maps to 0. That is why binary — with its two digits — is the natural language of electronics.

The DfE national curriculum for computing requires KS3 students to understand "how numbers can be represented in binary" as part of the broader topic of data representation (gov.uk/government/publications/national-curriculum-in-england-computing-programmes-of-study). This concept underpins how all data — text, images, video, sound — is ultimately stored.

The decimal system vs the binary system

To understand binary, it helps to look at the decimal system first.

In decimal (base 10), the place values are powers of 10:

… | 1000 | 100 | 10 | 1
… | 10³ | 10² | 10¹ | 10⁰

The number 435 means 4 × 100 + 3 × 10 + 5 × 1 = 435.

In binary (base 2), the place values are powers of 2:

128 | 64 | 32 | 16 | 8 | 4 | 2 | 1
2⁷ | 2⁶ | 2⁵ | 2⁴ | 2³ | 2² | 2¹ | 2⁰

Each column is worth exactly double the column to its right. You can only place a 0 or a 1 in each column.

How to convert binary to decimal

To convert a binary number to decimal, write the number under the place-value table and add up the values where a 1 appears.

Example: Convert 10110101 to decimal

128 | 64 | 32 | 16 | 8 | 4 | 2 | 1
1 | 0 | 1 | 1 | 0 | 1 | 0 | 1

Add the values where the digit is 1: 128 + 32 + 16 + 4 + 1 = 181

So 10110101 in binary equals 181 in decimal.

Practice table — five common conversions:

Binary | Working | Decimal
0001 | 1 | 1
0101 | 4 + 1 | 5
1000 | 8 | 8
1010 | 8 + 2 | 10
1111 | 8 + 4 + 2 + 1 | 15

How to convert decimal to binary

The standard method at KS3 is the repeated division by 2 method:

Divide the decimal number by 2 and note the remainder (0 or 1).

Divide the quotient by 2 and note the remainder.

Repeat until the quotient is 0.

Read the remainders from bottom to top — that is the binary number.

Worked example: Convert 25 to binary

Division | Quotient | Remainder
25 ÷ 2 | 12 | 1
12 ÷ 2 | 6 | 0
6 ÷ 2 | 3 | 0
3 ÷ 2 | 1 | 1
1 ÷ 2 | 0 | 1

Reading remainders from bottom to top: 11001

Check: 16 + 8 + 1 = 25. Correct.

An alternative method — often easier for small numbers — is to use the place-value table directly. Start at the largest place value that fits into your number, write a 1, subtract it, and repeat.

Example: Convert 42 to binary using place values

42 ≥ 32? Yes → write 1, remainder = 10

10 ≥ 16? No → write 0

10 ≥ 8? Yes → write 1, remainder = 2

2 ≥ 4? No → write 0

2 ≥ 2? Yes → write 1, remainder = 0

0 ≥ 1? No → write 0

Result: 101010

Check: 32 + 8 + 2 = 42. Correct.

Bits and bytes

A single binary digit (0 or 1) is called a bit — short for "binary digit." Bits are grouped together to represent larger values:

Term | Size | Maximum value
Bit | 1 binary digit | 1
Nibble | 4 bits | 15 (1111 in binary)
Byte | 8 bits | 255 (11111111 in binary)
Kilobyte (KB) | 1,024 bytes | —
Megabyte (MB) | 1,024 KB | —

With 8 bits (one byte), you can represent 2⁸ = 256 different values (0 to 255). This is why early computers stored text using 8-bit codes — the ASCII standard maps 256 characters including all English letters, digits and punctuation.

How binary represents text, images and sound

Understanding binary data representation is a key KS3 topic:

Text — each character is assigned a binary code. In ASCII, the letter A is 01000001 (65 in decimal). Modern text uses Unicode, which extends this to cover thousands of characters including Chinese, Arabic, and emoji.

Images — a black-and-white image is a grid of pixels; each pixel is stored as 0 (white) or 1 (black). Colour images use more bits per pixel to store colour information.

Sound — sound waves are sampled thousands of times per second; each sample is stored as a binary number representing the amplitude of the wave at that instant.

BBC Bitesize (bbc.co.uk/bitesize/guides/z26rcdm/revision/1) has interactive binary exercises that let students practise conversions and check their answers in real time.

Common mistakes in binary conversion

Reading remainders top to bottom instead of bottom to top in the division method — this gives a reversed (wrong) answer.

Forgetting to pad to 8 bits — when a question asks for an 8-bit binary number, shorter answers such as 11001 need to be padded with leading zeros to become 00011001.

Confusing binary 10 with decimal 10 — binary 10 equals decimal 2. Always state the base clearly when writing answers.

Frequently asked questions

What is binary in KS3 computing?

Binary is a base-2 number system that uses only the digits 0 and 1. Computers use binary because electronic circuits naturally have two states — on and off — which map directly to 1 and 0. At KS3, students learn to convert between binary and decimal and understand how binary is used to represent all types of data.

How do you convert binary to decimal at KS3?

Write the binary number under the place-value table (128, 64, 32, 16, 8, 4, 2, 1 from left to right for an 8-bit number). Add up the place values wherever a 1 appears. For example, 00001101 = 8 + 4 + 1 = 13.

What does a byte mean in computing?

A byte is a group of 8 bits. It can represent 256 different values (0 to 255 in decimal, or 00000000 to 11111111 in binary). A byte is the standard unit for measuring file sizes and memory, and is the building block of kilobytes, megabytes, and gigabytes.

Why is binary important for GCSE computer science?

Binary is the foundation of data representation — the topic that explains how computers store all information as numbers. At GCSE, students extend KS3 binary knowledge to cover hexadecimal, character encoding, image representation, and data compression. Strong KS3 foundations make these GCSE topics much more manageable.

What is the biggest number you can store in 8 bits?

With 8 bits, the highest value is 11111111 in binary, which equals 255 in decimal (128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 255). This is why 255 appears so often in computing — for example, each colour channel in RGB colour images has a value from 0 to 255.

For Socratic computing tutoring — from binary to Python — see aitutors.me.