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How is a binary code turned back into an analogue voltage, and how is the staircase output smoothed?

Digital-to-analogue conversion: the summing-amplifier (binary-weighted) DAC, the R-2R ladder, resolution and the analogue output, and reconstruction filtering.

An Eduqas A-Level Electronics answer on digital-to-analogue conversion: the binary-weighted summing-amplifier DAC, the R-2R ladder DAC, how the binary input sets the analogue output and its resolution, the staircase output, and the reconstruction (smoothing) filter.

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  1. What this dot point is asking
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What this dot point is asking

Eduqas wants you to describe digital-to-analogue conversion: the binary-weighted summing-amplifier DAC, the R-2R ladder, the resolution and analogue output, and reconstruction filtering. This is how a digital system speaks back to the analogue world.

The answer

The binary-weighted (summing-amplifier) DAC

The R-2R ladder DAC

Resolution and the analogue output

Reconstruction filtering

Examples in context

Digital-to-analogue conversion is how a digital system produces sound, control voltages and analogue signals: a music player's DAC turns stored samples back into the waveform that drives the amplifier and loudspeaker, and a microcontroller DAC sets a control voltage or generates a waveform. The summing amplifier here is exactly the op-amp circuit from the analogue module, and the reconstruction filter is a low-pass filter from the filters topic, tying signal conversion back to the earlier analogue work.

Try this

Q1. State how many output levels a 4-bit DAC has. [1 mark]

  • Cue. 24=162^4 = 16 levels.

Q2. State the main advantage of an R-2R ladder DAC over a binary-weighted DAC. [1 mark]

  • Cue. It uses only two resistor values, which are easy to match accurately.

Q3. State the purpose of the low-pass filter at a DAC output. [1 mark]

  • Cue. It smooths the staircase output into a continuous analogue signal (reconstruction).

Exam-style practice questions

Practice questions written in the style of WJEC Eduqas exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.

Eduqas 20206 marksA 4-bit binary-weighted DAC produces an output of 1.0 V1.0\ \text{V} for the least significant bit alone. Calculate the output voltage for the input code 10111011, and state the maximum (full-scale) output for 11111111.
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Weights (up to 2 marks): in a binary-weighted DAC each bit contributes a voltage proportional to its place value. With the LSB contributing 1.0 V1.0\ \text{V}, the bits (from LSB) contribute 1,2,4,8 V1, 2, 4, 8\ \text{V}.

Code 10111011 (up to 2 marks): the set bits are bit 0 (1 V1\ \text{V}), bit 1 (2 V2\ \text{V}) and bit 3 (8 V8\ \text{V}); bit 2 (4 V4\ \text{V}) is 00. Output =8+2+1=11 V= 8 + 2 + 1 = 11\ \text{V} (this matches the denary value 1111 of 10111011).

Full-scale 11111111 (up to 2 marks): all four bits set: 8+4+2+1=15 V8 + 4 + 2 + 1 = 15\ \text{V} (denary 1515).

Markers reward the binary-weighted contributions, the output 11 V11\ \text{V} for 10111011, and the full-scale 15 V15\ \text{V} for 11111111.

Eduqas 20225 marksState one disadvantage of the binary-weighted DAC, explain why the R-2R ladder is preferred, and state why a low-pass filter is placed at the DAC output.
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Binary-weighted disadvantage (up to 2 marks): it needs a wide range of precisely matched resistor values (each double the last), which is hard to manufacture accurately for many bits; small resistor errors in the most significant bits cause large output errors.

R-2R ladder (up to 2 marks): the R-2R ladder uses only two resistor values (RR and 2R2R) in a repeating network, which are far easier to match accurately, so it scales to many bits with good accuracy.

Reconstruction filter (up to 1 mark): the DAC output is a staircase that jumps at each new sample; a low-pass (reconstruction) filter smooths the steps into a continuous analogue signal and removes the high-frequency switching components.

Markers reward the wide spread of matched resistors as the binary-weighted weakness, the two-value R-2R network as the fix, and the smoothing/reconstruction low-pass filter at the output.

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