What does 4.5 Fundamentals of data representation cover?

It covers the decimal, binary and hexadecimal number systems and conversion between them, unsigned and signed (two's complement) integers, binary arithmetic, fixed and floating point representation of real numbers, bits and bytes and storage units, character encoding with ASCII and Unicode, representing images (bitmaps) and sound (sampling), and data compression, encryption and error checking.

Why do computers use binary and hexadecimal?

Computers use binary because their electronic components are two-state (on or off), which maps directly onto 1 and 0 and is reliable to detect. Hexadecimal is used as a human-friendly shorthand because each hex digit represents exactly four bits, so a byte is just two hex digits, making memory addresses, colour codes and machine values far easier to read than long strings of bits.

How does two's complement represent negative numbers?

Two's complement makes the most significant bit a negative place value (in 8 bits the leftmost column is minus 128), so one representation covers positive and negative numbers and the same circuit can add them. To negate a number you invert all the bits and add 1. Subtraction is done by adding the two's complement of the number being subtracted.

How is sound represented digitally?

Sound is a continuous analogue wave, so it is sampled: the amplitude is measured at regular intervals and stored as a binary number. Sample rate is samples per second (Hz) and sample resolution is the bits per sample. Higher values give better quality but larger files. File size in bits equals sample rate times sample resolution times duration (times the number of channels).

What is the difference between lossy and lossless compression?

Lossless compression removes redundancy so the exact original can be restored, using run length encoding or dictionary-based compression; it is needed for text and program files. Lossy compression permanently discards detail people are unlikely to notice, giving much smaller files for images, audio and video, but the original cannot be recovered.

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AQA A-Level Computer Science 4.5 Fundamentals of data representation: number systems, binary, characters, images, sound and compression

A deep-dive AQA A-Level Computer Science guide to 4.5 Fundamentals of data representation. Covers number systems and base conversion, signed binary in two's complement, fixed and floating point, bits and bytes, character encoding, representing images and sound, and data compression and encryption.

Generated by Claude Opus 4.818 min read4.5Updated 2026-06-02

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

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What 4.5 actually demands
Number systems and binary numbers
Bits, bytes and characters
Images, sound, compression and encryption
Check your knowledge

What 4.5 actually demands

Everything in a computer is stored as binary, and this module is how. AQA expects fluent, accurate conversions and calculations, so the skills must be automatic. The topics run from number bases through signed and real numbers, then how text, images and sound are encoded, and finally how data is compressed, encrypted and checked for errors.

Number systems and binary numbers

Convert confidently between decimal, binary and hexadecimal. Represent signed integers in two's complement (most significant bit negative; negate by inverting and adding 1), add and subtract in binary, and represent reals in fixed point (constant precision) or floating point (mantissa and exponent, larger range). Watch for overflow and rounding errors.

Bits, bytes and characters

A bit is one binary digit; a byte is 8 bits. Distinguish decimal prefixes (kilo $= 10^3$ ) from binary prefixes (kibi $= 2^{10} = 1024$ ), and remember $n$ bits give $2^n$ values. Character encoding maps characters to codes: ASCII uses 7 bits (128 codes), and Unicode was introduced to cover every writing system while staying backward compatible with ASCII.

Images, sound, compression and encryption

A bitmap image is pixels storing colour, with colour depth (bits per pixel) and resolution; file size $\approx$ width $\times$ height $\times$ colour depth. Sound is sampled at a sample rate and sample resolution. Lossless compression (run length encoding, dictionary-based) preserves the original; lossy discards detail. Symmetric encryption uses a shared key; asymmetric uses a public/private key pair. Parity bits and check digits detect errors.

Check your knowledge

Convert the binary number $1101\,0010$ to hexadecimal. (2 marks)
State why hexadecimal is used as a shorthand for binary. (1 mark)
Find the 8-bit two's complement representation of $-6$ . (2 marks)
State one advantage of floating point over fixed point. (1 mark)
State how many values can be represented in 6 bits, and the difference between a kilobyte and a kibibyte. (2 marks)
State why Unicode was introduced. (2 marks)
Calculate the file size in bits of a $100 \times 50$ image with colour depth 4 bits. (2 marks)
Encode the string WWWWWWBBB using run length encoding. (1 mark)

Solutions

Q1: $1101 = \text{D}$ and $0010 = 2$ , so the answer is $\text{D2}_{16}$ .
Q2: Each hexadecimal digit represents exactly four bits, so long binary numbers become much shorter and easier to read.
Q3: $+6 = 0000\,0110$ ; invert to $1111\,1001$ ; add 1 to get $1111\,1010$ .
Q4: It can represent a much larger range of numbers for the same number of bits.
Q5: $2^6 = 64$ values; a kilobyte is $10^3 = 1000$ bytes while a kibibyte is $2^{10} = 1024$ bytes.
Q6: ASCII could not represent the characters of other writing systems and many symbols, so Unicode was introduced to give a unique code to every character in every language.
Q7: $100 \times 50 \times 4 = 20\,000$ bits.
Q8: 6W3B.

Sources & how we know this

AQA A-level Computer Science (7517) specification — AQA (2015)