Analogue to Digital Conversion: The Basics Revision Notes | A Level AQA Physics

1. Why Convert Analogue to Digital?

Every time you stream music or make a phone call, your voice — a smoothly varying pressure wave — is being turned into a stream of 0s and 1s before it travels anywhere. That transformation is analogue-to-digital conversion (ADC), and understanding it sits at the heart of modern electronics.

The real world is analogue. Sound pressure, temperature, and light intensity all vary continuously and smoothly over time. Electronic circuits can represent these as continuously varying voltages — but continuously varying voltages are fragile. Noise, interference, and signal degradation all corrupt them during transmission.

Digital signals use only two voltage levels — a high level (representing binary 1) and a low level (representing binary 0). Because the receiver only needs to distinguish between two states rather than measure an exact voltage, digital signals are far more resistant to noise. This is the core motivation for converting analogue signals into digital form before transmission.

Now that the motivation is clear, the question becomes: how exactly do you turn a smooth, continuously varying voltage into a sequence of 0s and 1s? The answer involves three linked stages — sampling, quantisation, and binary encoding — each of which the AQA specification requires you to understand.

2. Sampling: Taking Snapshots of the Signal

Picture a microphone picking up a spoken word. The output voltage rises and falls smoothly, tracing the shape of the sound wave. To convert this into digital data, the ADC measures the voltage at regular time intervals — these measurements are called samples. The number of samples taken per second is the sampling rate, measured in hertz (Hz) or kilohertz (kHz).

Each sample captures the signal's voltage at one instant in time. Between samples, whatever the signal does is not recorded. This means sampling introduces a degree of approximation — the digital version is a series of snapshots, not a perfect copy of the original waveform.

For audio signals, the sampling rate must be at least twice the highest frequency present in the signal to avoid distortion (this is the Nyquist criterion, though AQA does not require you to recall the name). CD audio uses 44,100 samples per second — high enough to capture all frequencies the human ear can detect, up to about 20 kHz.

Sampling alone does not produce a digital signal — it produces a sequence of voltage measurements, each of which is still an analogue value. The next stage, quantisation, converts each measured voltage into one of a fixed set of discrete levels.

3. Quantisation: Rounding to Discrete Levels

Here is how to picture it. Imagine a ruler with only 8 marked positions between 0 V and 7 V. When the ADC measures a voltage of 3.7 V, it cannot record 3.7 — it rounds to the nearest mark, which might be 4 V. That rounding is quantisation. The difference between the true voltage (3.7 V) and the recorded level (4 V) is the quantisation error.

The number of discrete levels available depends directly on how many bits are used to encode each sample. With $n$ bits per sample, the number of quantisation levels is $2^n$. More bits means more levels, finer rounding, and smaller quantisation error — which translates to higher-quality audio reproduction.

Worked example: Calculating Quantisation Levels from Bit Depth

An ADC uses 4 bits per sample. Calculate the number of quantisation levels available.

1. $N = 2^n$ — N is the number of levels; n is the number of bits per sample. [M1]
2. $N = 2^4$ — n = 4 bits per sample. [M1]
3. $2^4 = 2 \times 2 \times 2 \times 2 = 16$ — Always expand powers longhand to avoid errors. [A1]
4. $N = 16$ quantisation levels — With 4 bits, the ADC can assign each sample to one of 16 discrete voltage levels.

Answer: 16 quantisation levels

Notice the pattern: every extra bit you add doubles the number of available levels. Going from 3 bits (8 levels) to 4 bits (16 levels) halves the maximum quantisation error. This is why professional audio uses 24-bit depth rather than the 16-bit depth of a CD — the improvement in precision is substantial.

4. Bits, Bytes, and Binary Numbers

Each quantisation level is assigned a unique binary number. A bit (binary digit) is the fundamental unit of digital information — it holds either a 0 or a 1, corresponding to the two voltage levels of a digital signal. Eight bits grouped together form one byte.

AQA requires you to recognise binary numbers from 1 to 10 — the table above covers exactly that range. You do not need to perform binary arithmetic; you need to know that each binary number is a pattern of 0s and 1s, and that each digit position represents a power of 2 (reading right to left: $2^0 = 1$, $2^1 = 2$, $2^2 = 4$, $2^3 = 8$).

When an ADC encodes a sample, it outputs the binary number corresponding to the quantisation level it has assigned. For example, if the ADC uses 4 bits and assigns a sample to level 6, it outputs the binary pattern 0110. That pattern is then transmitted as a sequence of high and low voltage pulses — the digital signal.

Connecting bits back to quantisation: if an ADC uses 8 bits per sample, it can represent $2^8 = 256$ quantisation levels, and each sample is transmitted as one byte of data. This direct link between bit depth, byte size, and signal quality is a key relationship to hold in mind.

5. The Full ADC Process: Putting It Together

Now that sampling, quantisation, and binary encoding are each clear individually, here is how they chain together in a real ADC system. The three stages happen in sequence, and each one feeds directly into the next.

Worked example: Tracing an Audio Signal Through an ADC

Describe and explain the three stages by which a microphone's analogue output is converted into a digital bitstream ready for transmission.

1. The ADC measures the analogue voltage at regular time intervals (e.g. 44,100 times per second for CD audio). — Each measurement captures the signal amplitude at one instant. The sampling rate determines how closely the digital version follows rapid changes in the original waveform.
2. Each measured voltage is rounded to the nearest of the $2^n$ available discrete levels. — This introduces a small quantisation error. More bits per sample means more levels and smaller errors, improving fidelity.
3. Each quantisation level is assigned a unique binary number (e.g. level 6 of 16 → 0110 in 4-bit encoding). — The binary number is transmitted as a sequence of high (1) and low (0) voltage pulses — the digital signal.
4. The digital bitstream travels through cables, fibre, or radio links to the receiver. — Because only two voltage states need to be distinguished, the signal can be regenerated cleanly at repeaters, removing accumulated noise — a key advantage over analogue transmission.

Answer: Analogue voltage → sampled at regular intervals → each sample quantised to nearest discrete level → level encoded as binary number → transmitted as digital high/low voltage pulses.

The chart above makes the doubling relationship vivid. Each additional bit doubles the number of levels, which is why the jump from 8 bits to 16 bits is so dramatic — from 256 levels to 65,536. Higher bit depth is the primary reason modern digital audio sounds smoother and more natural than early digital recordings.

6. Comparing Analogue and Digital Transmission

Earlier we established that digital signals resist noise better than analogue signals. It is worth being precise about why, because examiners frequently ask for an explanation rather than just a statement.

An analogue signal carries information in its exact voltage at every moment. Any noise added during transmission changes that voltage and therefore corrupts the information — there is no way to separate the original signal from the noise. A digital signal carries information only in whether the voltage is above or below a threshold. Noise must be large enough to push the voltage across that threshold before it causes an error, and amplifiers (called regenerators) along the transmission path can restore the signal to clean 0 and 1 levels before noise accumulates to that extent.

This is the fundamental advantage of digital transmission: the signal can be regenerated perfectly at each repeater, whereas an analogue signal can only be amplified — and amplification boosts the noise along with the signal.

7. Exam Technique and Common Mistakes

Questions on ADC appear in the Electronics section of AQA A Level Physics Paper 2. They tend to combine a short descriptive part (worth 2–3 marks) with a calculation using $N = 2^n$ (worth 1–2 marks). Knowing where marks are allocated helps you write efficiently.

When a question asks you to explain why digital signals are preferred for transmission, the mark scheme expects a causal chain: state that digital signals use only two voltage levels, then explain that noise must exceed the threshold between levels to cause an error, then conclude that the signal can be regenerated cleanly. A bare statement — 'digital signals are less affected by noise' — will not earn full marks without the mechanistic reasoning.

For calculation questions, always show the substitution $N = 2^n$ explicitly before evaluating the power. Expanding the power longhand (e.g. $2^4 = 2 \times 2 \times 2 \times 2 = 16$) avoids the common error of multiplying the base by the exponent ($2 \times 4 = 8$) rather than raising to the power.

Across this lesson, every AQA specification requirement for analogue-to-digital conversion has been addressed: the motivation for converting audio signals to digital form, the two-voltage-level representation, quantisation and the $N = 2^n$ relationship, the definitions of bits and bytes, and binary numbers from 1 to 10. Bring these ideas together and you have a complete, exam-ready account of how the analogue world becomes digital data.