Which of the following circuits has the same | vedclass

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(A) Let the inputs to the first $AND$ gate be $A$ and $\overline{B}$. The output is $P = A \cdot \overline{B}$.Let the inputs to the second $AND$ gate

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(A) Let the inputs to the first $AND$ gate be $A$ and $\overline{B}$. The output is $P = A \cdot \overline{B}$.Let the inputs to the second $AND$ gate be $A$ and $B$. The output is $Q = A \cdot B$.These outputs $P$ and $Q$ are fed into a $NOR$ gate.The final output $Y$ is given by:$Y = \overline{P + Q} = \overline{(A \cdot \overline{B}) + (A \cdot B)}$Using the distributive law,$Y = \overline{A \cdot (\overline{B} + B)}$Since $\overline{B} + B = 1$,we have $Y = \overline{A \cdot 1} = \overline{A}$.This corresponds to a $NOT$ gate with input $A$. $A$ $NAND$ gate with both inputs connected to $A$ acts as a $NOT$ gate,as its output is $\overline{A \cdot A} = \overline{A}$. Thus,option $A$ is correct.

Which of the following circuits has the same output as that of the given circuit?

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