Cambridge O-Level Computer Science: Data Representation (2210)

This guide covers Topic 1 Data Representation, the first of ten topics in Cambridge O-Level Computer Science (2210), for examination 2026-2028. The syllabus explicitly shares its content and topic structure with Cambridge IGCSE Computer Science (0478) – textbooks endorsed for 0478 are suitable for use with this O-Level too.

Where this fits in 2210

The ten topics are grouped into two broad strands: Computer systems (topics 1-6, which Data Representation opens) and Algorithms, programming and logic (topics 7-10). Understanding how data is represented underpins later topics on hardware, software and programming, where data types and storage limits recur constantly.

Syllabus coverage

CAMBRIDGE O-LEVEL COMPUTER SCIENCE (2210) — TOPIC 1 DATA REPRESENTATION

CAMBRIDGE O-LEVEL COMPUTER SCIENCE (2210) — TOPIC 1 DATA REPRESENTATION

• 1.1 Number systems — denary, binary and hexadecimal, converting between them, binary addition and overflow, logical binary shifts, and two’s complement for negative integers
• 1.2 Text, sound and images — how and why a computer represents text using character sets, sound (sample rate and resolution), and images (resolution and colour depth)
• 1.3 Data storage and compression — data storage units from bit to exbibyte, calculating file size, and lossy and lossless compression

Sitting alongside Data transmission, Hardware, Software, The internet and its uses, and Automated and emerging technologies within the Computer systems strand, Data Representation covers how numbers, text, sound and images are represented and stored in binary form inside a computer system, including the compression of data to reduce storage and transmission requirements.

How to approach it

Binary and hexadecimal number conversion is a foundational skill tested throughout this syllabus, not just within Topic 1, so practise converting between denary, binary and hexadecimal until it is fluent rather than something you have to work out from first principles under exam pressure. This O-Level’s own syllabus breaks the topic into the same three numbered strands as the sibling 0478 syllabus — number systems, text/sound/image representation, and data storage and compression — so structuring your revision around those three strands follows the syllabus’s own structure directly. Understanding why compression matters (storage and transmission efficiency) rather than just the mechanics of an algorithm also strengthens answers on the more applied questions this topic can generate.

Official syllabus

Cambridge O-Level Computer Science (2210) syllabus for examination 2026-2028 — cambridgeinternational.org.

Number systems

Computers store everything as binary because a circuit has two reliable states. Hexadecimal is used as a shorthand for humans: one hex digit maps exactly to four binary digits, so long binary strings become readable.

Denary 205  ->  Binary 11001101  ->  Hex CD

128 64 32 16  8  4  2  1
  1  1  0  0  1  1  0  1     = 128+64+8+4+1 = 205

Split into nibbles: 1100 = 12 = C,  1101 = 13 = D  ->  CD

Hexadecimal appears in MAC addresses, IP version 6 addresses, colour codes and memory dumps — knowing where it is used is examinable alongside the conversion.

Binary arithmetic and overflow

Add binary as in denary, carrying when a column reaches 2. Overflow occurs when the result needs more bits than the register holds — adding two 8-bit numbers giving a 9-bit answer. The extra bit is lost and the stored result is wrong.

A logical shift left multiplies by two, a shift right divides by two. Bits shifted out are lost, which is another route to inaccuracy.

Text, sound and images

Text is stored using character sets. ASCII uses 7 bits for 128 characters, extended ASCII 8 bits for 256, and Unicode covers a very wide range of the world’s writing systems — a fixed-width Unicode encoding uses more bits per character than ASCII, though UTF-8 (the most common Unicode encoding) keeps plain ASCII characters at one byte.

Sound is captured by sampling the analogue wave. Sample rate is how many samples per second, sample resolution is the number of bits per sample. Raising either improves accuracy and increases file size.

Images are stored as pixels. Resolution is the number of pixels, colour depth the bits per pixel. A higher colour depth allows more colours: n bits gives 2^n colours.

Image file size = width x height x colour depth (in bits)
Sound file size = sample rate x sample resolution x seconds

Compression

Lossless compression removes redundancy so the original can be perfectly reconstructed — run-length encoding, and essential for text and program files where any loss would corrupt the data.

Run-length encoding (RLE) works by replacing runs of identical, repeated values with a single value and a count of how many times it repeats, so highly repetitive data — such as a simple image with large blocks of a single colour — is stored far more compactly. RLE can, however, sometimes produce a larger file than the original: on noisy or photographic data, where pixel values rarely repeat exactly, encoding each short run as a (value, count) pair can take more space than simply storing the original values, which is why RLE suits simple graphics far better than continuously varying photographic images.

Lossy compression permanently discards data the user is unlikely to notice, giving much smaller files — acceptable for photographs, music and video, unacceptable for a spreadsheet.

Worked example

An image is 800 by 600 pixels with a colour depth of 24 bits. Find the file size in mebibytes (MiB).

bits  = 800 x 600 x 24 = 11 520 000 bits
bytes = 11 520 000 / 8 = 1 440 000 bytes
KiB   = 1 440 000 / 1024 = 1406.25 KiB
MiB   = 1406.25 / 1024   = 1.37 MiB

Dividing by 8 to reach bytes, then by 1024 twice, is where most errors occur.

Common mistakes

Confusing sample rate with sample resolution. Dividing by 1000 rather than 1024 when converting bytes to kibibytes, or labelling the answer KB or MB instead of KiB or MiB. Forgetting to convert bits to bytes at all. Saying lossy compression “removes unnecessary data” without noting it is permanent. Describing hexadecimal as something the computer stores — the machine stores binary; hex is for human readability.

Quick revision checklist

• Convert between denary, binary and hexadecimal in both directions.
• Add binary numbers, and explain overflow and logical shifts.
• Compare ASCII, extended ASCII and Unicode.
• Calculate image and sound file sizes with correct unit conversion.
• Distinguish lossless from lossy compression and justify which suits a given file type.