Which one of the following will be the output | vedclass

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(D) The circuit consists of an $AND$ gate,an $OR$ gate,a $NOT$ gate,and a final $AND$ gate.$1$. The output of the first $AND$ gate is $A \cdot B$. Thi

Vedclass · Accepted Answer

$\overline{A} B + A \overline{B}$

Vedclass · Answer

(D) The circuit consists of an $AND$ gate,an $OR$ gate,a $NOT$ gate,and a final $AND$ gate.$1$. The output of the first $AND$ gate is $A \cdot B$. This is passed through a $NOT$ gate,so the input to the final $AND$ gate is $\overline{A \cdot B}$.$2$. The output of the $OR$ gate is $A + B$. This is the second input to the final $AND$ gate.$3$. The final output $Y$ is the $AND$ operation of these two inputs:$Y = (\overline{A \cdot B}) \cdot (A + B)$Using De Morgan's theorem,$\overline{A \cdot B} = \overline{A} + \overline{B}$:$Y = (\overline{A} + \overline{B}) \cdot (A + B)$$Y = \overline{A} \cdot A + \overline{A} \cdot B + \overline{B} \cdot A + \overline{B} \cdot B$Since $\overline{A} \cdot A = 0$ and $\overline{B} \cdot B = 0$:$Y = 0 + \overline{A} B + A \overline{B} + 0$$Y = \overline{A} B + A \overline{B}$

Which one of the following will be the output of the given circuit?

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