ITPEC FE Morning April 2018 Question 21
A D/A converter with a resolution of 8 bits generates an output voltage of 0 volts for a digital input value of 0, and an output voltage of 2.5 volts for a digital input value of 128. When the lowest 1 bit of the digital input value is changed, which of the following is the change (in volts) of the output voltage that is generated by the D/A converter?
Explanation
2.5/128 V (about 0.0195 V) — the output is linear in the input value, so one step of the lowest bit is the voltage per unit of input.
The converter gives 0 V for input 0 and 2.5 V for input 128. Going from 0 to 128 is 128 equal steps, so each step is worth 2.5 ÷ 128 V. Changing the lowest bit changes the input value by exactly 1, so the output changes by one step.
Check: 128 × (2.5 ÷ 128) = 2.5 V, which matches the given data point.
Answer (a)
Why not others:
- •(b) 2.5/255 — assumes 2.5 V is the full-scale output at the largest 8-bit input 255; then input 128 would give only about 1.25 V, not 2.5 V
- •(c) 2.5/256 — spreads 2.5 V over all 256 levels of an 8-bit converter; then input 128 would give 128 × 2.5 ÷ 256 = 1.25 V, contradicting the given 2.5 V
- •(d) 2.5/512 — a step four times too small; input 128 would give 128 × 2.5 ÷ 512 = 0.625 V
Key rule: For a linear converter, the step per least significant bit is the voltage difference between two given points divided by the difference in their input values; use the points given rather than an assumed full scale.
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