The diagram of a logic circuit is given below | vedclass

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Question

(A) The circuit consists of two $OR$ gates followed by an $AND$ gate.$1$. The output of the first $OR$ gate with inputs $W$ and $X$ is $(W + X)$.$2$.

Vedclass · Accepted Answer

$W + (X \cdot Y)$

Vedclass · Answer

(A) The circuit consists of two $OR$ gates followed by an $AND$ gate.$1$. The output of the first $OR$ gate with inputs $W$ and $X$ is $(W + X)$.$2$. The output of the second $OR$ gate with inputs $W$ and $Y$ is $(W + Y)$.$3$. These two outputs are fed into an $AND$ gate,so the final output is $(W + X) \cdot (W + Y)$.$4$. Expanding this expression using Boolean algebra:$	ext{Output} = (W + X) \cdot (W + Y)$$= W \cdot W + W \cdot Y + X \cdot W + X \cdot Y$$= W + W \cdot Y + W \cdot X + X \cdot Y$$= W(1 + Y + X) + X \cdot Y$Since $(1 + Y + X) = 1$,we get:$= W + X \cdot Y$

The diagram of a logic circuit is given below. The output of the circuit is represented by:

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