GATE 2025 EC – Question 35
A 4-bit weighted-resistor DAC with inputs $b_3$, $b_2$, $b_1$, and $b_0$ (MSB to LSB) is designed using an ideal opamp, as shown below. The switches are closed when the corresponding input bits are logic ‘1’ and open otherwise.
When the input $b_3b_2b_1b_0$ changes from 1110 to 1101, the magnitude of the change in the output voltage $V_O$ (in mV, rounded off to the nearest integer) is ________.
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Correct answer: 250
Explanation
The summing amplifier gives $V_O=-V_{REF}\dfrac{R_f}{R}\left(b_3+\dfrac{b_2}{2}+\dfrac{b_1}{4}+\dfrac{b_0}{8}\right)=-2\left(b_3+\dfrac{b_2}{2}+\dfrac{b_1}{4}+\dfrac{b_0}{8}\right)$ with $R_f=R$. For 1110: $-2(1+0.5+0.25)=-3.5$ V. For 1101: $-2(1+0.5+0.125)=-3.25$ V. The change has magnitude 0.25 V = 250 mV.