Calculate the file size in bytes of a 100 × 100 pixel image at 8 bits per pixel. [2 marks]

EnglandComputer ScienceSyllabus dot point

How are text, images and sound represented as binary, and what determines the file size and quality?

Representing text, images and sound: character sets (ASCII and Unicode), bitmap images with resolution, colour depth and the file-size calculation, and sampled sound with sample rate, bit depth and the file-size calculation.

An Eduqas Component 2 answer on representing text, images and sound: the ASCII and Unicode character sets, bitmap images with resolution and colour depth and the file-size calculation, and sampled sound with sample rate and bit depth and the file-size calculation.

Generated by Claude Opus 4.814 min answerUpdated 2026-06-02

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

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Quick answer

Text is represented by a character set mapping each character to a binary code. ASCII uses $7$ bits ( $128$ characters), enough for English; extended ASCII uses $8$ bits ( $256$ ). Unicode uses more bits (up to $32$ ) to represent every character in every language plus emoji, at the cost of larger files. Images are stored as bitmaps: a grid of pixels, each holding a colour. Resolution is the number of pixels (width $\times$ height); colour depth is the bits per pixel ( $n$ bits gives $2^n$ colours). The file size in bits is $\text{width} \times \text{height} \times \text{colour depth}$ (then divide by $8$ for bytes). Sound is sampled: the analogue wave's amplitude is measured at regular intervals and each measurement stored as a binary number. Sample rate is samples per second (Hz); bit depth is bits per sample. The file size in bits is $\text{sample rate} \times \text{duration} \times \text{bit depth}$ (times the number of channels, then divide by $8$ ). Higher resolution, colour depth, sample rate and bit depth give better quality but larger files.

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What this dot point is asking

Eduqas wants you to explain how text, images and sound are represented in binary: the character sets (ASCII and Unicode), bitmap images (resolution, colour depth and the file-size calculation), and sampled sound (sample rate, bit depth and the file-size calculation). The image and sound file-size calculations are examined frequently.

The answer

Representing text: ASCII and Unicode

Representing images: bitmaps and file size

Representing sound: sampling and file size

Key fact

Sound is analogue, so it is sampled to be stored digitally: the wave's amplitude is measured at regular intervals and each measurement recorded as a binary number. The sample rate is the number of samples per second, measured in hertz (Hz); a higher rate captures higher frequencies (CD audio uses $44\,100$ Hz). The bit depth is the number of bits used to store each sample; a higher bit depth records the amplitude more precisely (more dynamic range). The file size in bits is $\text{sample rate} \times \text{duration in seconds} \times \text{bit depth}$ , multiplied by the number of channels (mono $= 1$ , stereo $= 2$ ), then divided by $8$ for bytes. Higher sample rate and bit depth give better fidelity but larger files.

Calculate image and sound file sizes

Find the file size of a $300 \times 200$ pixel image at $8$ bits colour depth, and of a $5$ second stereo sound clip at $44\,100$ Hz with $16$ -bit depth.

step 1: Image, total bits

Pixels $= 300 \times 200 = 60\,000$ . Bits $= 60\,000 \times 8 = 480\,000$ bits.

step 2: Image, convert to bytes

$480\,000 \div 8 = 60\,000$ bytes (about $58.6$ KB).

step 3: Sound, total bits

Samples per channel $= 44\,100 \times 5 = 220\,500$ . Stereo has $2$ channels, so total samples $= 220\,500 \times 2 = 441\,000$ . Bits $= 441\,000 \times 16 = 7\,056\,000$ bits.

step 4: Sound, convert to bytes

$7\,056\,000 \div 8 = 882\,000$ bytes (about $861$ KB). Both calculations follow the same pattern: count the units, multiply by bits per unit, divide by $8$ .

Examples in context

These representations underlie every file you use: a text document (character set), a photo (bitmap resolution and colour depth) and a music track (sample rate and bit depth). The file-size calculations explain why a high-resolution photo or a high-fidelity audio file is large, and why compression (the next dot point) is so important for storage and transmission. Unicode is why modern software can display any language and emoji. The binary skills from the number-systems dot point are exactly what is being counted in these file-size sums.

Try this

Q1. How many colours can a colour depth of $5$ bits represent? [1 mark]

Cue. $2^5 = 32$ colours.

Q2. Calculate the file size in bytes of a $100 \times 100$ pixel image at $8$ bits per pixel. [2 marks]

Cue. $100 \times 100 \times 8 = 80\,000$ bits; $\div 8 = 10\,000$ bytes.

Q3. Define sample rate. [1 mark]

Cue. The number of samples (amplitude measurements) taken per second, measured in hertz (Hz).

Exam-style practice questions

Practice questions written in the style of WJEC Eduqas exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.

Eduqas 20195 marksA bitmap image is

200

pixels wide and

150

pixels high, using a colour depth of

4

bits per pixel. Calculate the file size in bytes (ignoring any header), showing your working, and state what is meant by colour depth.

Show worked answer →

Colour depth (up to 1 mark): the number of bits used to represent the colour of each pixel; $n$ bits gives $2^n$ possible colours.

File-size calculation (up to 4 marks): number of pixels $= 200 \times 150 = 30\,000$ . Bits $= 30\,000 \times 4 = 120\,000$ bits. Bytes $= 120\,000 \div 8 = 15\,000$ bytes.

Markers reward the bits-per-pixel definition of colour depth, multiplying width by height by colour depth for the total bits, and dividing by $8$ to get $15\,000$ bytes. A common error is forgetting to divide by $8$ .

Eduqas 20216 marksExplain how sound is represented digitally by sampling, define sample rate and bit depth, and calculate the file size of a

10

second mono recording sampled at

44\,100

Hz with a bit depth of

16

bits.

Show worked answer →

Sampling (up to 2 marks): the analogue sound wave's amplitude is measured (sampled) at regular intervals and each measurement is stored as a binary number; more frequent, finer samples reproduce the wave more accurately.

Definitions (up to 1 mark): sample rate is the number of samples taken per second (in Hz); bit depth is the number of bits used to store each sample.

File-size calculation (up to 3 marks): samples $= 44\,100 \times 10 = 441\,000$ . Bits $= 441\,000 \times 16 = 7\,056\,000$ bits. Bytes $= 7\,056\,000 \div 8 = 882\,000$ bytes (mono, so one channel).

Markers reward the sample-the-amplitude-at-intervals description, correct definitions, and sample rate $\times$ duration $\times$ bit depth, divided by $8$ , giving $882\,000$ bytes.

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Sources & how we know this

WJEC Eduqas GCE AS/A Level Computer Science specification (from 2015) — Eduqas (2015)