GATE CS 2020 Q.29 (CS Q.19): Combinational Circuits

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 _______.

Your answer

Official answer and solution

Official answer: 5
From: Official GATE 2020 answer key

Solution

Use the relationship between input lines and select lines for an N-to-1 multiplexer.

An $N$ -to-1 multiplexer has $N$ data inputs and selects exactly one input line to forward to the output line.

To distinguish among $N$ distinct inputs, the number of select lines $k$ must satisfy:

2^k \ge N

Here, $N = 32$ registers:

2^k \ge 32 \implies k = \log_2 32 = 5

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

Final answer

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

Source

Paper: GATE 2020 Computer Science and Information Technology (CS)
Question: 29 of 65, printed as CS Q.19
Section: Computer Science and Information Technology

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