Discussion
An 8-bit DAC is used to control a linear valve with a 0 to 5 volt signal. The valve is fully open if the signal is 5 volts and closed if signal is 0 volt. An approximate resolution of the DAC in terms of volts and percentage of valve opening will be :
Answer: A
The resolution is about 0.02 V and 0.4%.
An 8-bit DAC has \(2^{8} = 256\) levels, so its 0-5 V range is divided into 255 steps:
\[ \begin{aligned} \Delta V &= \frac{5}{255} \approx 0.0196\ \text{V} \approx 0.02\ \text{V} \\ \% &= \frac{1}{255} \times 100 \approx 0.39\% \end{aligned} \]
Since the valve opening is linear in the voltage, one step moves it about 0.4% of its full travel. 4% and 10% are ten or more times too coarse for 8 bits, and 0.01 V would need about 9 bits.
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