Consider the digital circuit shown below with two input lines A and B, two…
2026
Consider the digital circuit shown below with two input lines A and B, two select lines S0 and S1, and an output line Y. The blocks Q and M represent active high 2:4 decoder and 4-to-1 multiplexer, respectively. Out of 16 possible input combinations, the number of combinations that produce Y=1 is ____________. (answer in integer) Note: One input combination is an instance of [A B S1 S0]
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Correct answer: 6
First, analyze the 2:4 Decoder (Q). With inputs A and B, the output D0 is high (1) when A=0 and B=0. The output D3 is high (1) when A=1 and B=1.
Next, analyze the 4-to-1 Multiplexer (M). The select lines are S1 and S0. The inputs are: I0=D0, I1=0, I2=1, I3=D3.
The output Y depends on S1 and S0 as follows:
- If S1=0, S0=0, Y selects I0 (D0). Y=1 when A=0, B=0. (1 combination)
- If S1=0, S0=1, Y selects I1 (0). Y is always 0. (0 combinations)
- If S1=1, S0=0, Y selects I2 (1). Y is always 1 regardless of A and B. (4 combinations)
- If S1=1, S0=1, Y selects I3 (D3). Y=1 when A=1, B=1. (1 combination)
Total combinations where Y=1: 1 + 0 + 4 + 1 = 6.
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