The diagram of a logic circuit is given below | vedclass

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Question

(D) The circuit consists of two $OR$ gates followed by an $AND$ gate.
Let the inputs to the first $OR$ gate be $W$ and $Y$. Its output is $(W + Y)$.

Vedclass · Accepted Answer

$W + (X . Y)$

Vedclass · Answer

(D) The circuit consists of two $OR$ gates followed by an $AND$ gate.
Let the inputs to the first $OR$ gate be $W$ and $Y$. Its output is $(W + Y)$.
Let the inputs to the second $OR$ gate be $W$ and $X$. Its output is $(W + X)$.
These two outputs are fed into an $AND$ gate.
Therefore, the final output $Z = (W + Y) . (W + X)$.
Using the distributive law of Boolean algebra: $Z = W . W + W . X + Y . W + Y . X$.
Since $W . W = W$, we have $Z = W + W . X + W . Y + X . Y$.
Factoring out $W$: $Z = W . (1 + X + Y) + X . Y$.
Since $(1 + X + Y) = 1$, we get $Z = W . (1) + X . Y = W + X . Y$.

The diagram of a logic circuit is given below. Find the output of the circuit.

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