Image Representation: Pixels and Colour Depth

A pixel (picture element) is a single point in a digital image. Every digital image stored on a computer is made up of a rectangular grid of pixels — this type of image is called a bitmap.

Each pixel stores a single colour value as a binary number. When the pixels are small enough and packed tightly enough, the human eye perceives a continuous image rather than a grid of discrete dots.

Property	What it means
Pixel	One point in the image, storing one colour value
Bitmap	An image stored as a grid of pixel colour values
Image dimensions	The width and height of the grid, measured in pixels
Colour depth	The number of bits used to represent each pixel's colour

A black-and-white image uses 1 bit per pixel (0 = white, 1 = black). A full-colour image typically uses 24 bits per pixel — 8 bits each for red, green, and blue channels.

A pixel has no fixed physical size. The same 800 × 600 pixel image printed on a postcard looks sharp; stretched across a billboard it looks blocky. The number of pixels does not change — only the physical size of each one does.

An image's dimensions are expressed as width × height in pixels. Multiplying width by height gives the total pixel count — the number of individual colour values that must be stored.

Examples:

Image	Width (px)	Height (px)	Total pixels
Thumbnail	100	100	10,000
Standard HD	1280	720	921,600
Full HD	1920	1080	2,073,600
4K UHD	3840	2160	8,294,400

A higher total pixel count captures more spatial detail. A 1920 × 1080 image contains roughly 200 times more pixels than a 100 × 100 thumbnail. However, resolution alone does not determine file size — colour depth also plays a critical role.

Colour depth is the number of bits used to represent each pixel. More bits per pixel means more possible colour values, producing a more detailed and realistic image.

The number of possible colours is $2^{\text{colour depth}}$:

Colour depth (bits)	Possible colours	Example use
1	2	Black and white
4	16	Early computer graphics
8	256	Simple web graphics
16	65,536	High colour
24	16,777,216	True colour (typical photographs)

Worked example — how many colours can a 4-bit image represent?

$2^4=16\text{ possible colours}$

A 4-bit image can only assign one of 16 colours to each pixel. Switching to 8-bit doubles the number of bits but squares the number of available colours from 16 to 256.

The uncompressed file size of a bitmap image depends on three values: width, height, and colour depth.

$\text{File size (bits)}=\text{width}\times \text{height}\times \text{colour depth}$

$\text{File size (bytes)}=\frac{\text{width}\times \text{height}\times \text{colour depth}}{8}$

Worked example — calculate the file size of a 200 × 300 image with 8-bit colour depth:

$\frac{200\times 300\times 8}{8}=\frac{480,000}{8}=60,000\text{ bytes}$

Worked example — calculate the file size of a 640 × 480 image with 24-bit colour depth:

$\frac{640\times 480\times 24}{8}=\frac{7,372,800}{8}=921,600\text{ bytes}=921.6\text{ kB}$

The formula gives the uncompressed file size. Real image files (JPEG, PNG) are smaller because compression is applied — but the uncompressed value is what AQA 8525 expects you to calculate.

A black-and-white bitmap (1 bit per pixel) can be read directly from its binary data. Each bit maps to one pixel: 0 = white, 1 = black.

Worked example — decode this 4 × 4 bitmap:

Row	Binary	Pixels (W = white, B = black)
1	0000	W W W W
2	0110	W B B W
3	0110	W B B W
4	0000	W W W W

The pattern forms a 2 × 2 black square in the centre of an all-white frame.

Encoding works in reverse: given a pixel grid, write 0 for each white pixel and 1 for each black pixel, reading left to right across each row.

Both resolution and colour depth affect file size proportionally — doubling either one doubles the file size.

Change	Effect on file size	Effect on quality
Double the width and height	× 4 (quadruple)	More spatial detail
Double the colour depth	× 2 (double)	More colour accuracy
Halve the colour depth	÷ 2 (halve)	Fewer colours, visible banding
Reduce resolution	Decreases	Loss of fine detail

Worked example — compare two versions of a 100 × 100 image:

Version	Colour depth	File size
A	8-bit	$(100\times 100\times 8)÷8=10,000\text{ bytes}$
B	24-bit	$(100\times 100\times 24)÷8=30,000\text{ bytes}$

Version B stores the same number of pixels but uses three times the storage because each pixel carries three times as many bits. These trade-offs drive decisions about compression and storage in real systems.

1. Forgetting to divide by 8

The formula $\text{width}\times \text{height}\times \text{colour depth}$ gives the file size in bits. Divide by 8 to convert to bytes. Leaving the answer in bits will lose the mark.

2. Confusing colour depth with number of colours

Colour depth is measured in bits. Number of colours is $2^{\text{colour depth}}$. A colour depth of 8 bits gives 256 colours — not 8 colours.

3. Saying higher resolution always produces better quality

A high-resolution image with a low colour depth can look worse than a lower-resolution image with a high colour depth. Both dimensions of quality matter independently.

4. Misreading binary bitmaps

Read binary pixel data left to right, treating each bit as one pixel. The most common error is reading a 0 as black and a 1 as white — or vice versa to what the question specifies. Check the question's convention before decoding.

5. Using total pixel count as the file size

Total pixel count (width × height) is not the file size. File size also depends on colour depth. A 100 × 100 image with 1-bit colour is 1,250 bytes; the same resolution with 24-bit colour is 30,000 bytes.