GATE EC 2022 Set 1 — Question 19
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Digital Circuits → Combinational Logic → MUX, DEMUX, Decoders & Encoders
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Question
Consider the 2-bit multiplexer (MUX) shown in the figure. For OUTPUT to be the XOR of C and D, the values for , and are ________.
Correct answer
(C) A₀ = 0, A₁ = 1, A₂ = 1, A₃ = 0
Solution
A 2-bit multiplexer (MUX) has two select lines, and , and four data inputs, . The output of the MUX is given by the equation:In this problem, the select lines are C and D, so we set and . The desired output is the XOR of C and D, which is .We can determine the required values for by comparing the MUX output with the desired XOR output for all possible combinations of C and D:
The desired XOR output is .
Therefore, .
The desired XOR output is .
Therefore, .
The desired XOR output is .
Therefore, .
The desired XOR output is .
Therefore, .Combining these results, we get .This matches option (C).The final answer is
1.When :
The select lines are . The MUX output is .The desired XOR output is .
Therefore, .
2.When :
The select lines are . The MUX output is .The desired XOR output is .
Therefore, .
3.When :
The select lines are . The MUX output is .The desired XOR output is .
Therefore, .
4.When :
The select lines are . The MUX output is .The desired XOR output is .
Therefore, .Combining these results, we get .This matches option (C).The final answer is
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