Consider a digital logic circuit consisting of three 2-to-1 multiplexers M1,…
2024
Consider a digital logic circuit consisting of three 2-to-1 multiplexers M1, M2, and M3 as shown below. X1 and X2 are inputs of M1. X3 and X4 are inputs of M2. A, B, and C are select lines of M1, M2, and M3, respectively.
For an instance of inputs X1=1, X2=1, X3=0, and X4=0, the number of combinations of A, B, C that give the output Y=1 is _________
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Correct answer: 4
Answer: 4
Explanation:
Compute the output of the first multiplexer (M1): it selects X1 when A = 0 and X2 when A = 1. Given X1 = 1 and X2 = 1, the output of M1 (call it Q1) is 1 for both values of A.
Compute the output of the second multiplexer (M2): it selects X3 when B = 0 and X4 when B = 1. Given X3 = 0 and X4 = 0, the output of M2 (call it Q2) is 0 for both values of B.
The final multiplexer (M3) selects Q1 when C = 0 and Q2 when C = 1. Since Q1 = 1 and Q2 = 0, the final output Y is 1 exactly when C = 0.
A can be 0 or 1 (2 choices)
B can be 0 or 1 (2 choices)
C must be 0 (1 choice) for Y = 1
Total combinations = 2 × 2 × 1 = 4
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