GATE 2026 CS (CS2) – Question 59
Consider the digital circuit shown below with two input lines $A$ and $B$, two select lines $S_0$ and $S_1$, and an output line $Y$. The blocks $Q$ and $M$ represent an active-high 2:4 decoder and a 4-to-1 multiplexer, respectively. Out of the 16 possible input combinations, the number of combinations that produce $Y=1$ is __________. (answer in integer)
Note: One input combination is an instance of $[A\ B\ S_1\ S_0]$.
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Correct answer: 6
Explanation
Analyze the circuit by the select inputs. For $S=00$, the multiplexer selects $D_0$, which is 1 only when $AB=00$, giving 1 combination. For $S=01$, it selects a constant 0, giving 0 combinations. For $S=10$, it selects a constant 1, giving all 4 possible values of $AB$. For $S=11$, it selects $D_3$, which is 1 only when $AB=11$, giving 1 combination. Therefore, the total number of input combinations yielding $Y=1$ is $1+0+4+1=6$. This question depends on the circuit figure.