GATE EC 2024 Set 1 — Question 41
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Digital Circuits → Combinational Logic → MUX, DEMUX, Decoders & Encoders
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Question
The propagation delay of the MUX shown in the circuit is . Consider the propagation delay of the inverter as .
If is set to then the output is _______.
Correct answer
(B) a square wave of frequency 50 MHz
Solution
The given circuit is a multiplexer with a feedback loop. The output is fed back through an inverter. Based on the circuit diagram, the inverter is placed on the feedback path before it splits to both data inputs and . Therefore, and . The output of the MUX is given by the logic expression .
Substituting , we get:
.This means the output will toggle its state after every propagation delay through the loop, regardless of the value of . The total propagation delay in the feedback loop is:
.Since the output toggles every , a full cycle (e.g., ) takes:
.The frequency of the resulting square wave is:
.Thus, when , the output is a square wave of frequency .
Substituting , we get:
.This means the output will toggle its state after every propagation delay through the loop, regardless of the value of . The total propagation delay in the feedback loop is:
.Since the output toggles every , a full cycle (e.g., ) takes:
.The frequency of the resulting square wave is:
.Thus, when , the output is a square wave of frequency .
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