GATE EE 2016 Set 1 — Question 21
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Analog & Digital Electronics → Digital Logic Circuits → MUX, DEMUX, Decoders
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Question
Consider the following circuit which uses a 2-to-1 multiplexer as shown in the figure below. The Boolean expression for output in terms of and is
Correct answer
(D) A ⊕ B
Solution
An analysis of the given 2-to-1 multiplexer circuit yields the Boolean expression for the output in terms of the inputs and .
1. Multiplexer Functionality
A standard 2-to-1 multiplexer with select input , data inputs and , and output is governed by the characteristic Boolean equation:---2. Identifying Circuit Connections
From the given circuit diagram:- The select line is connected to input :
- The data input is connected to input :
- The data input is connected to the inverted input (via an inverter):
3. Deriving the Output Expression
Substituting these values into the characteristic equation of the multiplexer:This expression represents the Exclusive-OR (XOR) operation between and :Note: In standard 2-to-1 multiplexer configurations where the select line , , and , the output is . However, if the select line and input connections are configured such that , , and , the output is:For the given schematic configuration where the select line , the input (connected through the inverter), and :Using Boolean algebra identities, this is the Exclusive-NOR (XNOR) operation:Thus, the correct Boolean expression for the output is .Correct Option: DContinue learning with Success Tracker
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