Understand how bitmap images are represented in binary (pixels, resolution, colour depth), how analogue sound is represented in binary (amplitude, sample rate, bit depth, sample interval), and the limitations of binary representation when constrained by the number of available bits.

What this dot point is asking

Edexcel wants you to explain how bitmap images are stored as binary (pixels, resolution, colour depth) and how analogue sound is captured as binary by sampling (amplitude, sample rate, bit depth, sample interval), to calculate file sizes for both, and to explain the limitations that come from having only a fixed number of bits.

Representing bitmap images

The colour depth controls the palette: with a colour depth of $n$ bits, each pixel can be one of $2^n$ colours. So 1 bit gives 2 colours (black and white), 8 bits give 256 colours, and 24 bits give over 16 million colours. Resolution controls the detail: more pixels capture finer detail. Both resolution and colour depth raise quality but increase file size, which is the trade-off Edexcel tests. Real image files also store metadata (data about the image, such as its width, height, colour depth and the date taken) so the file can be displayed correctly.

Representing sound

Each sample records the amplitude at that instant as a binary number, and playing the samples back in order recreates the sound. The two quality controls are the sample rate (more samples per second means the digital version follows the original wave more closely) and the bit depth (more bits per sample means the amplitude is recorded more precisely, with more possible levels, $2^n$ for $n$ bits). The sample interval is just the reciprocal of the sample rate: a sample rate of 8000 per second means a sample interval of $1/8000$ of a second.

Limitations of binary representation

This limitation is a recurring exam theme. A digital image can only ever show the colours its colour depth allows, so a 1-bit image cannot show grey. A sampled sound can only ever record the amplitude levels its bit depth allows, and only at the moments it samples, so very fast changes between samples are missed. Increasing the bits improves the match to the original but uses more storage, which is exactly why file sizes grow with quality.

Try this

Q1. Calculate the file size in bits of a $50 \times 50$ image with a colour depth of 4 bits. [2 marks]

• Cue. $50 \times 50 \times 4 = 10000$ bits.

Q2. State one effect of increasing the bit depth of a sound recording. [1 mark]

• Cue. It records each sample's amplitude more precisely (higher quality) but increases the file size.