Fundamentals of Data Representation — AQA GCSE Computer Science

Computers store and process all data as binary. This unit covers number systems, units and how text, images and sound are represented.

Number systems

Computers use binary (base 2). You should be able to convert between:

Denary (base 10) ↔ binary (base 2) ↔ hexadecimal (base 16).

Hexadecimal is used because it is shorter and easier for humans to read than long binary numbers, and each hex digit represents exactly 4 bits (a nibble).

Binary arithmetic

Binary addition of two 8-bit numbers (watch for overflow when the result is too big for the bits available).
Binary shifts — a left shift multiplies by 2 each place; a right shift divides by 2.

Units of information

Bit = a single 0 or 1; nibble = 4 bits; byte = 8 bits.
Multiples: kilobyte (kB), megabyte (MB), gigabyte (GB), terabyte (TB) — each ×1000.
Be able to calculate file sizes.

Representing text

Characters are represented by character sets: ASCII (7 bits, 128 characters) and Unicode (more bits, supports many languages and symbols). Each character has a numeric code.

Representing images

A bitmap image is made of pixels, each stored as a binary colour value. Image quality depends on resolution (number of pixels) and colour depth (bits per pixel). File size = width × height × colour depth (in bits). Metadata stores extra information (e.g. dimensions).

Representing sound

Sound is sampled at intervals (analogue → digital). Quality and file size depend on the sample rate (samples per second) and sample resolution (bits per sample). Higher values give better quality but larger files.

Compression

Lossless compression — reduces size with no loss of data (original can be perfectly restored).
Lossy compression — reduces size more by removing some data (cannot be perfectly restored).

Exam tips

Practise denary ↔ binary ↔ hex conversions and binary addition/shifts.
Learn the units (bit, nibble, byte, kB…) and file-size calculations.
Image size = width × height × colour depth; sound depends on sample rate and resolution.
Distinguish lossless vs lossy compression.