How Sound Is Represented in Binary: GCSE Computing

Sound is a continuous analogue wave, but computers can only store binary numbers, so digital audio is created by sampling the wave thousands of times per second. GCSE computer science requires you to explain sampling rate and bit depth, and to calculate the file size of a recording from both values.

What is the difference between analogue and digital sound?

Real sound travels as a continuous wave of changing air pressure — it has no gaps or steps, and in theory it could take infinitely many values. A computer cannot store something continuous; it can only store discrete binary numbers. To turn sound into something a computer can save, a device called an analogue-to-digital converter (ADC) measures the height, or amplitude, of the sound wave at regular moments in time. Each measurement is called a sample, and each sample is stored as a binary number.

Played back through a digital-to-analogue converter (DAC), those stored samples are turned back into a continuous electrical signal that drives a speaker — which is how a phone or computer reproduces sound from a file.

What is sampling rate and how is it measured?

The sampling rate is how many samples are taken every second, measured in hertz (Hz) or kilohertz (kHz, thousands of hertz). A higher sampling rate takes more measurements of the wave per second, capturing its shape more accurately.

The general rule GCSE specifications expect you to know is that the sampling rate needs to be high enough to capture the changes in the original wave — too low a sampling rate and quiet details or high-pitched sounds are lost between samples, producing a noticeably worse recording.

What is bit depth and how does it affect sound quality?

Bit depth (sometimes called sample resolution) is the number of bits used to store each individual sample. More bits means each sample can record a more precise amplitude value, in exactly the same way that more bits per pixel allows an image to store more precise colour.

How do you calculate the file size of a digital audio recording?

The formula GCSE questions expect is:

$$\text{file size (bits)} = \text{sampling rate} \times \text{bit depth} \times \text{duration (seconds)} \times \text{channels}$$

Channels means 1 for mono (a single sound stream) or 2 for stereo (separate left and right streams).

Worked example 1 (mono): A 5-second mono recording is sampled at 44,100 Hz with a bit depth of 16 bits. What is the file size in bytes?

• 44,100 samples/second × 16 bits/sample × 5 seconds × 1 channel
• = 44,100 × 16 × 5 = 3,528,000 bits
• File size = 3,528,000 ÷ 8 = 441,000 bytes ≈ 430.7 KB

Worked example 2 (stereo): A 3-second stereo recording is sampled at 8,000 Hz with a bit depth of 8 bits. What is the file size in bytes?

• 8,000 samples/second × 8 bits/sample × 3 seconds × 2 channels
• = 8,000 × 8 × 3 × 2 = 384,000 bits
• File size = 384,000 ÷ 8 = 48,000 bytes ≈ 46.9 KB

Comparing the two examples shows how every factor in the formula matters: the second recording is shorter and has a much lower sampling rate and bit depth, yet the doubled channel count and the multiplication of all four factors together still determine the final size — always work through the formula term by term rather than trying to estimate.

Why does higher quality always mean a bigger file?

Sampling rate, bit depth, duration and channel count are multiplied together, so increasing any one of them increases file size in direct proportion. Doubling the sampling rate doubles the file size for the same recording; doubling the bit depth also doubles it. This is the fundamental trade-off in digital audio: better-sounding recordings need more storage and more bandwidth to transmit.

In practice, most music and voice files you download or stream are compressed using formats such as MP3, which remove sound detail the human ear is unlikely to notice in order to shrink the file dramatically. Compression is a related but separate GCSE topic — the sampling rate and bit depth calculations above describe the size of the raw, uncompressed audio data before any compression is applied.

Frequently asked questions

How do you calculate the file size of a sound recording?

Multiply the sampling rate (in Hz) by the bit depth (in bits), by the duration in seconds, and by the number of channels (1 for mono, 2 for stereo). This gives the file size in bits; divide by 8 to convert to bytes. For example, a 2-second mono clip sampled at 8,000 Hz with 8-bit depth uses 8,000 × 8 × 2 × 1 = 128,000 bits, which equals 16,000 bytes.

What is the difference between sampling rate and bit depth?

Sampling rate is how often the sound wave is measured per second, measured in hertz — it affects how accurately changes in the sound over time are captured. Bit depth is how precisely each individual measurement is stored, measured in bits — it affects how accurately the volume, or amplitude, of each sample is recorded. Both affect sound quality and file size independently.

Why does a low sampling rate make a recording sound worse?

A low sampling rate means the sound wave is measured only occasionally, so rapid or subtle changes in the wave between samples are missed entirely. This is particularly noticeable for high-pitched sounds and fine detail, which is why telephone-quality audio at 8,000 Hz sounds noticeably duller and less clear than CD-quality audio at 44,100 Hz.

What is the difference between mono and stereo recording?

Mono recording uses a single audio channel, so the same sound is played through every speaker. Stereo recording uses two channels — left and right — to create a sense of direction and space in the sound. Stereo recordings need twice the data of an equivalent mono recording, because both channels must be sampled and stored separately.

For Socratic GCSE computer science tutoring on data representation, from binary to digital audio, visit aitutors.me.