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GATE 2020 IN – Question 51

Digital Electronics · ADC and DAC: Analog multiplexer, programmable gain amplifier, sample-and-hold, ADCs (successive approximation, integrating, flash, sigma-delta), DACs (weighted R, R-2R ladder, current steering), dynamic range, resolution, INL, DNL, ENOB · 2 marks · Numerical answer

A 10-bit DAC has 1.023 V full-scale output. Its address inputs $A_9\ldots A_2$ connect to an 8-bit microprocessor’s $D_7\ldots D_0$, while $A_1,A_0$ are grounded. If the processor byte changes from 1010 1010 to 1010 1011, find output change in mV, to one decimal place.

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Correct answer: 3.5 to 4.5

Explanation

The processor byte increases by one, but its least significant bit drives DAC bit A₂, worth four DAC counts. The DAC step is $1.023/(2^{10}-1)=0.001$ V = 1 mV. Therefore the output changes by $4(1)=4.0$ mV. Grounding the two lowest bits prevents ordinary one-count DAC steps.

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