A multiplexer is placed between a group of 32 registers and an accumulator to regulate data movement such that at any given point in time the content of only one register will move to the accumulator. The minimum number of select lines needed for the multiplexer is ________.

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Official answer: 5 (±0)

Combinational and Sequential Circuits

To select one register out of $N = 32$ registers, the multiplexer must have $N = 32$ input lines (or input channels).

A multiplexer with $2^k$ input lines requires $k$ select lines to uniquely choose one input:

2^k = 32 \implies k = \log_2(32) = 5

Therefore, the minimum number of select lines needed is 5.

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This Combinational and Sequential Circuits previous year question is Q19 of the GATE CSE 2020 paper. Find more GATE CSE PYQs on Combinational and Sequential Circuits in Digital Logic, or browse all GATE CSE PYQs.

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