AQA A-Level Computer Science (7517)

## Learning Outcomes

- Understand how computers store images, sound and related file information as binary bit patterns
- Explain the difference between analogue and digital data, and how conversion between them works
- Calculate uncompressed bitmap image sizes using resolution and colour depth
- Calculate uncompressed sound file sizes using sample rate, sample resolution, duration and channels
- Apply **Nyquist theorem** to find the minimum valid sampling rate
- Compare bitmap images, vector graphics and MIDI in terms of storage, quality and typical uses
- Identify the role of metadata and file headers in helping software interpret stored data
- Avoid common exam errors involving units, formulas and confused terminology

## AQA A-Level Computer Science (7517) Syllabus

For the AQA A-Level Computer Science (7517), you are expected to understand how images, sound and related file data are represented in binary form, with a focus on the following syllabus points:

- Know that all media data is stored as **bit patterns**, whose meaning depends on the encoding used
- Identify the difference between **analogue** and **digital** data and signals
- Explain how **digitisation** works, including sampling, quantisation, sample rate and sample resolution
- Understand and apply **Nyquist theorem** to determine the minimum sampling rate
- Calculate uncompressed file sizes for bitmap images and sampled sound
- Compare **bitmap images** with **vector graphics** in terms of representation, scalability and storage
- Explain the purpose of **metadata** and a **file header** in image and sound files
- Understand the uses of **lossy** and **lossless** compression, and the purpose of **MIDI**

## Test Your Knowledge

_Attempt these questions before reading this article. If you find some difficult or cannot remember the answers, look more closely at that area during your revision._

1. What is the difference between analogue data and digital data?
2. How do resolution and colour depth affect the size of a bitmap image?
3. What is the difference between sample rate and sample resolution in sound?
4. Why does stereo sound usually take twice as much storage as mono sound?
5. What is stored in metadata or a file header, and why does it matter?

## Introduction

Computers do not store pictures as “pictures” or sound as “sound”. They store everything as binary: sequences of 0s and 1s. The exam tests whether you understand how those bit patterns can be interpreted in different ways to represent media such as images and audio.

![Binary encoding of bitmap images, sampled audio, and associated metadata using resolution, colour depth, sample rate, and sample resolution.](https://static.pastpaperhero.com/images/aqa-a-level-computer-science-7517-data-representation-representing-images-sound-and-other-data_00.png)

_Image and sound data are presented as discrete bit patterns with parameters that determine storage size and reconstruction accuracy._

This topic is easy to revise badly because students often remember a few formulas but do not really understand what the numbers mean. In the exam, that causes errors such as mixing up image resolution with sound resolution, or sample rate with bit depth. To score well, you need both the definitions and the reasoning behind them.

> **Key Term: bit pattern**
> A sequence of bits used to represent data. Its meaning depends on the encoding or format being used.

### Analogue, digital and digitisation

A useful starting point is the distinction between **analogue** and **digital**.

Real-world data is often analogue. Sound waves, light intensity and temperature all vary continuously. That means there are infinitely many possible values between two points. If you draw analogue data on a graph, it usually appears as a smooth curve.

Digital data is different. It uses a limited set of discrete values. Computers work with binary, so values must be represented in fixed patterns of bits. On a graph, digital data is often shown as steps rather than a smooth wave.

> **Key Term: analogue data**
> Data that varies continuously and can take any value within a range.
>
> **Key Term: digital data**
> Data that uses discrete values and is represented in binary inside a computer system.

Why can a computer not store analogue data directly? Because memory and storage devices are built from components with distinct states, such as on/off. So analogue input must first be converted into digital form.

This is the job of an **analogue-to-digital converter (ADC)**. For sound, an ADC measures the amplitude of the analogue wave at regular intervals. Each measurement is then converted into a binary value. When audio is played back, a **digital-to-analogue converter (DAC)** turns those stored binary values back into an analogue signal that a speaker can output.

> **Key Term: analogue-to-digital converter (ADC)**
> Hardware that converts continuous analogue input into digital binary data.
>
> **Key Term: digital-to-analogue converter (DAC)**
> Hardware that converts stored digital values into an analogue signal for output.

Digitisation has two main parts that students must keep separate:

1. **Sampling**: taking measurements at regular time intervals
2. **Quantisation**: rounding each measurement to the nearest available digital value

Quantisation matters because a digital system cannot store every possible analogue value. If sample resolution is low, there are fewer available levels, so the rounded value may differ more from the original wave. That reduces accuracy.

> **Key Term: quantisation**
> The process of mapping a measured analogue value to the nearest available digital level.

A higher sample rate improves time accuracy because the waveform is measured more often. A higher sample resolution improves amplitude accuracy because each sample can be stored more precisely. These are different improvements, and exam questions often test whether you can distinguish them.

> **Test Tip:** If a question asks what improves the “frequency detail” or how well changes over time are captured, think **sample rate**. If it asks about the precision of each measured value, think **sample resolution** or **bit depth**.

### Representing images: bitmap and vector graphics

There are two important ways to represent images: **bitmap images** and **vector graphics**.

A bitmap image stores the colour of each individual pixel in a grid. A pixel is the smallest addressable part of the image. If an image is 800 × 600, it contains 480,000 pixels, and each one needs stored colour data.

> **Key Term: bitmap image**
> An image stored as a grid of pixels, where each pixel has a binary-coded colour value.
>
> **Key Term: pixel**
> The smallest addressable element of a bitmap image.

Two key measures affect bitmap storage:

- **Resolution**: the image dimensions in pixels, such as 1920 × 1080
- **Colour depth**: the number of bits used to store each pixel’s colour
  > **Key Term: resolution**
  > The dimensions of an image in pixels, usually expressed as width × height.
  >
  > **Key Term: colour depth**
  > The number of bits used to represent the colour of each pixel.

Colour depth determines how many colours are possible using the rule:

number of colours = 2^(colour depth)

So:

- 1 bit gives 2 colours
- 2 bits gives 4 colours
- 8 bits gives 256 colours
- 24 bits gives 16,777,216 colours

That 24-bit figure is common because many systems use 8 bits for red, 8 bits for green and 8 bits for blue in the RGB model.

The uncompressed bitmap file size formula is:

file size in bits = width × height × colour depth

Then convert bits to bytes by dividing by 8.

Worked example:

An image is 1200 px × 800 px with a colour depth of 24 bits.

Step 1: Find total number of pixels

1200 × 800 = 960,000 pixels

Step 2: Multiply by colour depth

960,000 × 24 = 23,040,000 bits

Step 3: Convert to bytes

23,040,000 ÷ 8 = 2,880,000 bytes

Step 4: If needed, convert to KB or MB using binary units

2,880,000 ÷ 1024 = 2812.5 KB  
2812.5 ÷ 1024 ≈ 2.75 MB

So the uncompressed image size is about 2.75 MB, ignoring metadata and any compression.

Why do higher resolution and colour depth improve quality? Resolution increases the number of pixels available to describe detail. Colour depth increases the number of colours each pixel can show. But both also increase file size because more bits must be stored.

Students often confuse resolution with image quality in a vague way. A better answer is specific: increasing resolution improves spatial detail; increasing colour depth improves colour accuracy.

Bitmap images are good for photographs because photos contain fine detail, complex shading and irregular patterns. A pixel grid handles that well, even though it can require a large file.

Vector graphics work differently. Instead of storing every pixel, they store mathematical descriptions of shapes called **vector primitives**, such as lines, curves, circles and polygons, with properties such as coordinates, line colour and fill colour.

> **Key Term: vector graphic**
> An image represented by mathematical descriptions of shapes rather than individual pixels.
>
> **Key Term: vector primitive**
> A basic shape or object, such as a line, circle or polygon, used to build a vector image.

Because a vector image stores drawing instructions, it can be scaled up without pixelation. The computer simply redraws the shapes at the new size. That makes vector graphics ideal for logos, diagrams and icons.

Bitmap and vector images are often compared in exams:

- Bitmap: better for photos, larger files, pixelates when enlarged
- Vector: better for logos/diagrams, smaller files for simple images, scales cleanly

But vector is not always “better”. For a photo, describing every shade and irregular edge as geometric objects would be inefficient and impractical.

> **Test Tip:** In “compare bitmap and vector” questions, do not just list one advantage of each. Explain why the storage method causes the advantage. For example, vector graphics scale well because they store shape properties, not fixed pixels.

### Representing sound: sampling, resolution and Nyquist theorem

Sound in the real world is analogue. A microphone turns sound waves into an analogue electrical signal. To store that sound on a computer, the signal must be sampled and digitised.

The computer does not store the whole smooth wave directly. Instead, it measures the amplitude of the wave at fixed intervals.

> **Key Term: sampling rate**
> The number of sound samples taken per second, measured in hertz (Hz).
>
> **Key Term: sample resolution**
> The number of bits used to store each sample value.

Sample rate affects how often the sound wave is measured. Sample resolution affects how precisely each measurement is stored.

For example:

- A higher **sample rate** captures more points along the waveform each second
- A higher **sample resolution** allows more possible amplitude levels for each sample

If either is too low, sound quality falls. Low sample rate can miss changes in the waveform. Low sample resolution can make the amplitude values less accurate.

This leads to **Nyquist theorem**, which is a regular exam topic.

> **Key Term: Nyquist theorem**
> The rule that the minimum sampling rate must be at least twice the highest frequency present in the original analogue signal.

Why twice? Because a wave must be sampled often enough to capture its shape. If you sample too slowly, different waves can produce the same stored samples, so the original frequency cannot be reconstructed properly.

If the highest frequency present is 15,000 Hz, then the minimum sample rate is:

2 × 15,000 = 30,000 Hz

For human hearing, the upper range is about 20 kHz, so a sample rate above 40 kHz is needed for faithful recording of the full range. This is why CD-quality audio uses 44.1 kHz.

Now the file size formula:

sound file size in bits = sample rate × sample resolution × duration × number of channels

Mono has 1 channel. Stereo has 2 channels.

Worked example:

A 90-second stereo recording uses a sample rate of 44,100 Hz and a sample resolution of 16 bits.

Step 1: Multiply sample rate by sample resolution

44,100 × 16 = 705,600 bits per second per channel

Step 2: Multiply by channels

705,600 × 2 = 1,411,200 bits per second

Step 3: Multiply by duration

1,411,200 × 90 = 127,008,000 bits

Step 4: Convert to bytes

127,008,000 ÷ 8 = 15,876,000 bytes

Step 5: Convert to MB if needed

15,876,000 ÷ 1024 ÷ 1024 ≈ 15.14 MB

So the recording takes about 15.14 MB uncompressed.

Common mistakes in this topic:

- forgetting the stereo factor of 2
- forgetting to divide by 8 to convert bits to bytes
- mixing up Hz and kHz
- stating Nyquist as “equal to the highest frequency” instead of “twice”

### Other data: metadata, file headers, compression and MIDI

An image or sound file does not just contain the main image pixels or sound samples. It also includes information that tells software how to interpret those bits.

> **Key Term: metadata**
> Data about data, such as dimensions, colour depth, duration or date created.
>
> **Key Term: file header**
> The part of a file that stores identifying and format information needed to interpret the rest of the file.

For an image, metadata or header data may include:

- width and height
- colour depth
- file format
- date created
- device used
- GPS location

For a sound file, it may include:

- sample rate
- sample resolution
- number of channels
- duration
- compression type

This matters because the same raw bit pattern could be interpreted differently if the software does not know the format. A header helps the system know what kind of file it is reading and how to decode it correctly.

Compression reduces file size. This can save storage space and reduce transmission time.

- **Lossless compression** keeps all original data, so decompression recreates the exact original file
- **Lossy compression** permanently removes some data, so decompression does not restore a perfect original

Lossless compression is suitable where exact recovery matters, such as text, program files and many data files. It is also used for some image and audio formats. Lossy compression is common for images, audio and video where some quality loss is acceptable in return for a much smaller file.

You should also know **MIDI**.

> **Key Term: MIDI**
> A format for representing musical performance instructions such as note, pitch, duration and instrument, rather than storing sampled sound waves.

MIDI files are usually very small because they do not store the full waveform. They store instructions like “play middle C for half a second using piano”. This makes them easy to edit. You can change tempo, pitch or instrument without rerecording the piece.

But MIDI is not suitable for vocals or natural sound recordings because it does not capture the real waveform. Playback quality also depends on the device and sound library being used.

A standard exam distinction is:

- sampled audio stores the actual sound wave data
- MIDI stores instructions for generating notes

## Key Point Checklist

_This article has covered the following key knowledge points:_

- Computers store images, sound and related media information as binary bit patterns
- Analogue data is continuous, while digital data is discrete
- An ADC converts analogue input to digital data, and a DAC converts digital data back to analogue output
- Digitisation of sound involves sampling and quantisation
- Bitmap images are stored as grids of pixels, while vector graphics are stored as shape descriptions
- Image resolution is width × height in pixels, while colour depth is the number of bits per pixel
- Uncompressed bitmap size in bits = width × height × colour depth
- Sound quality depends on both sampling rate and sample resolution
- Nyquist theorem states that the minimum sample rate must be at least twice the highest frequency present
- Uncompressed sound size in bits = sample rate × sample resolution × duration × channels
- Metadata is data about data, and a file header stores information needed to interpret a file
- MIDI stores musical instructions rather than sampled audio, so files are small but not suitable for natural recordings

## Key Terms and Concepts

- bit pattern
- analogue data
- digital data
- analogue-to-digital converter (ADC)
- digital-to-analogue converter (DAC)
- quantisation
- bitmap image
- pixel
- resolution
- colour depth
- vector graphic
- vector primitive
- sampling rate
- sample resolution
- Nyquist theorem
- metadata
- file header
- MIDI


Data Representation - Representing images, sound and other data