What number work do I need for Eduqas GCSE Computer Science?

You need to convert between binary, denary and hexadecimal in every direction, add two 8-bit binary numbers and spot overflow, perform left and right binary shifts (which multiply or divide by powers of two), and use two's complement for negative numbers. You also need the units of data and the formulas for image file size (width times height times colour depth) and sound file size (sample rate times bit depth times seconds). None of it uses a calculator, so the methods must be automatic.

How do I calculate the size of an image file?

The file size in bits is width times height times colour depth. Multiply the pixel dimensions to get the total pixels, multiply by the colour depth (bits per pixel) to get total bits, then divide by 8 for bytes and by 1000 for each step up to kilobytes or megabytes. Always finish in the unit the question asks for, and show every line of working because the marks are split across the steps.

What is two's complement and why is it used?

Two's complement is the standard way to store negative whole numbers in binary. The most significant bit is given a negative place value (minus 128 in an 8-bit number), so a leading 1 means negative and a leading 0 means positive. To make a negative, write the positive in binary, invert every bit, then add 1. It is used because ordinary binary addition still works on the signed values, so the hardware does not need a separate method for subtraction.

What is the difference between lossy and lossless compression?

Lossy compression permanently removes some data to make a much smaller file, so the original cannot be fully restored; it suits photos and music where a small quality drop is acceptable. Lossless compression removes no data, so the original is reconstructed exactly, usually with a smaller size saving; it suits text, spreadsheets and program files where every bit must survive. Run-length encoding is a lossless method that stores runs of repeated values as a value plus a count.

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Data representation and storage overview - Eduqas GCSE Computer Science

A deep-dive guide to data representation and storage in Eduqas GCSE Computer Science: binary, denary and hexadecimal conversion, binary addition and shifts, two's complement, ASCII and Unicode, the units of data, image and sound file-size calculations, and compression.

Generated by Claude Opus 4.812 min readEduqas GCSE CS 1.10 Data representationUpdated 2026-06-02

Reviewed by: AI editorial process; not yet individually human-reviewed

Jump to a section

Number systems and binary arithmetic
Representing text, images and sound
Compression
How to revise this topic

This module is the number-and-data heart of Component 1: how computers store numbers, text, images and sound in binary, and how to do the calculations the exam asks for. It is the most calculation-heavy topic, and the marks reward clear working. Each section links to a focused answer page with worked Eduqas questions.

Number systems and binary arithmetic

Computers store everything in binary (base 2). Denary (base 10) is our everyday system and hexadecimal (base 16) is a shorthand where each hex digit equals four bits, so one byte is two hex digits. You must convert between all three: see the number systems page.

Binary addition is column-by-column with carrying, and overflow happens when the result needs more bits than are available. Binary shifts move the bits left (multiplying by powers of two) or right (dividing by powers of two). Both are on the binary addition and shifts page.

To store negatives, the computer uses two's complement, where the leftmost bit has a negative place value: write the positive, invert the bits, add one. The 8-bit range is minus 128 to plus 127. See the two's complement page.

Representing text, images and sound

Text is stored using a character set that maps each character to a binary code. ASCII uses 7 bits (128 codes), enough for English; Unicode uses more bits to cover the world's writing systems and emoji, keeping the first 128 codes the same as ASCII. See the ASCII and Unicode page.

Images are grids of pixels: file size is width times height times colour depth (bits per pixel). Sound is sampled: file size is sample rate times bit depth times seconds. The units of data (bit, nibble, byte, KB, MB, GB, TB) and full worked file-size calculations are on the units and file-size page.

Compression

Compression shrinks files to save space and speed up transfers. Lossy compression permanently removes data for a big size saving (JPEG, MP3); lossless compression keeps every bit so the original is restored exactly (ZIP, PNG), and run-length encoding is a simple lossless method for repetitive data. See the compression page.

How to revise this topic

Drill conversions until they are automatic. Binary to denary to hexadecimal in every direction, with the place values written out, is worth easy marks if it is fast and accurate.
Practise the calculations to the right unit. Image and sound file sizes are method-marked; finish in bytes, KB or MB as asked, never leaving the answer in bits.
Memorise the two's complement method. Invert then add one, and remember the leftmost bit is negative; the 8-bit range is minus 128 to plus 127.
Learn the compression contrast. Lossy versus lossless, with a sensible use for each, is a recurring four-mark question.

Test yourself with the data representation and storage quiz, then work through each dot-point page for the full worked exam questions.