Bits and bytes — A bit is a binary digit with value 0 or 1. A byte contains eight bits. The same pattern can mean different things depending on how a program interprets it, such as a number, a character code or part of an image. Binary digits do not carry their own labels; a format or agreed encoding supplies the interpretation.
Place value — Unsigned binary represents zero and positive whole numbers without reserving a bit for a minus sign. Its place values double moving left: 1, 2, 4, 8, 16 and so on, the powers of two. In 1011, the 1s select 8, 2 and 1, giving decimal 11. State the number base: binary 10 represents decimal 2, not decimal ten.Four unsigned bits have weights 8, 4, 2 and 1; 1011 selects 8, 2 and 1 to represent decimal 11. Full-size diagram
Decimal to binary — To represent decimal 13 using four unsigned bits, choose 8, then 4, skip 2 and choose 1. This gives 1101 because 8 + 4 + 1 = 13. Check by converting back. Four unsigned bits represent values from 0 to 15; extra leading zeroes do not change the value but the available width limits the largest representable number.
Binary addition — Add from the right: 0 + 0 gives 0; 0 + 1 gives 1; 1 + 1 gives 10, so write 0 and carry 1 to the next column. For 0101 + 0011, the result is 1000, corresponding to 5 + 3 = 8. Include any carried value when adding the next column.
Overflow and limits — In a fixed four-bit unsigned representation, 1111 is 15. Adding 0001 produces mathematical 10000, which needs five bits. If a system keeps only four bits, the carry is lost and the stored pattern does not represent 16. A representation's limits are design choices; a computer cannot store an unlimited range in a fixed number of bits.
Boolean logic
Boolean values — Boolean logic uses two values: true and false. The condition temperature > 20 is true at 25 and false at 15. Electronic circuits use physical signals, such as higher and lower voltage ranges, to represent two logical states. Printed 0s and 1s are our notation, not tiny written numbers travelling down a wire. Boolean logic is a simplified model of how these two-state rules work.
AND and OR — AND is true only when both inputs are true; OR is true when at least one is true, including when both are true. For inputs 0,0 the outputs are 0,0; for 0,1 they are 0,1; for 1,0 they are 0,1; for 1,1 they are 1,1. This OR is inclusive, rather than meaning 'one or the other but not both'.AND requires both inputs to be 1. Inclusive OR is 1 for either or both inputs being 1. Full-size diagram
NOT and combined conditions — NOT reverses a Boolean value: NOT true is false and NOT false is true. In a model alarm, trigger = door_open AND NOT authorised. The alarm triggers only when the door is open and authorisation is false. Use brackets or intermediate named conditions to make combined expressions clear, and test every relevant input combination.
Truth tables and circuits — A truth table lists all input combinations and their outputs. Two Boolean inputs have four combinations, while three have eight. A simple circuit combines logic gates implementing operations such as AND, OR and NOT. Relate each gate to the rule it implements; a circuit diagram without a tested input-output relationship does not establish correctness.
Text and pictures
Text encoding — Text encoding agrees how characters are stored as numbers. A reader needs the same encoding to turn stored data back into the intended text; otherwise characters may appear corrupted. ASCII covers a limited set of characters, while Unicode covers many languages and symbols.
Code points and UTF-8 — A Unicode code point is a number identifying a character or part of a written symbol. UTF-8 stores these numbers using bytes. Some code points need more than one byte, and a visible symbol can combine code points, so character count does not always equal byte count. For example, a text with 10 characters is not automatically a 10-byte file.
Pixels and resolution — A raster image stores a grid of pixels, each with colour information. Pixel dimensions such as 100 × 80 describe 8,000 pixels. Increasing dimensions can preserve more spatial detail when genuine source detail exists, but enlarging a small image cannot recover information that was never captured. Display size and pixel count are related but different concepts.
Colour depth and storage — Colour depth is the number of bits used for each pixel’s colour in this simplified model. Two bits have four patterns: 00, 01, 10 and 11, allowing four colours. Eight bits allow 256 patterns. A 100 × 80 image has 8,000 pixels; at eight bits each that is 64,000 bits. Divide by eight bits per byte to get 8,000 bytes, excluding headers and other file information.
Image manipulation — Cropping removes an area, resizing changes pixel dimensions and adjusting colour changes stored pixel values. A destructive edit can discard useful detail, so keep an original and an appropriately named working copy. Select dimensions and format for the audience and purpose, then inspect the output rather than assuming every smaller file is equally usable.
Vector graphics — A vector image describes shapes and paths mathematically rather than storing only a fixed pixel grid. It can scale cleanly for a simple diagram or logo, though the screen still renders pixels. Raster images suit many photographs; vectors suit many clean schematics. Choose according to content and editing needs rather than claiming one format is best for every visual.
Sound and compression
Sampling sound — Digital recording measures a changing sound signal at regular intervals. Amplitude describes the signal’s size at each sample; quantising means rounding measurements to available stored levels. Sample rate is the number of measurements per second. Bit depth controls how many amplitude levels can be stored for each measurement. These affect different aspects of recording detail and accuracy, or fidelity. The values approximate a signal; a file does not contain tiny physical sounds.
Sound storage calculation — Mono uses one sound channel; stereo uses two. For simplified uncompressed mono data: raw bits = samples per second × bits per sample × seconds. So 8,000 × 8 × 2 = 128,000 bits. Divide by eight to get 16,000 bytes. Stereo doubles that raw amount because it stores two channels. Headers, information stored about the file, and compression can make the actual file size differ.
Compression choices — Lossless compression reduces storage while allowing exact reconstruction; lossy compression discards some information to reduce size further. Lossy changes may be unobtrusive for one purpose but unsuitable for another. Compare the exported result with the original, including legibility or sound quality. Repeated lossy re-saving can compound loss; a filename extension alone does not prove quality.
Digital manipulation and meaning — Programs manipulate binary data according to instructions and formats, allowing text editing, image transforms and sound processing. The fact that a file is digital does not establish that its content is accurate or authentic. Record sources and edits when they matter, and distinguish a simulation or illustration from evidence of an event.
Test yourself
50 questions · Random sets of 10. These quick checks support revision; practise longer explanations and justified judgements too.
Mind map
Use the branches to recall the ideas and explain their connections. Check the revision notes for the full detail.
KS3COMP3 · 1
View KS3COMP3 · 1 mind mapOpen the full-size map to zoom. Use the printable view for A4 landscape or enlarge to A3.
Mr Kidman's Classroom
