The given logic circuit is equivalent to whic | vedclass

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(C) The circuit consists of an $OR$ gate and a $NAND$ gate whose outputs are fed into an $AND$ gate.Let the inputs be $A$ and $B$.The output of the $O

Vedclass · Accepted Answer

$XOR$

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(C) The circuit consists of an $OR$ gate and a $NAND$ gate whose outputs are fed into an $AND$ gate.Let the inputs be $A$ and $B$.The output of the $OR$ gate is $(A + B)$.The output of the $NAND$ gate is $(\overline{A \cdot B})$.The final output $Y$ of the $AND$ gate is:$Y = (A + B) \cdot (\overline{A \cdot B})$Using De Morgan's theorem,$\overline{A \cdot B} = \overline{A} + \overline{B}$.So,$Y = (A + B) \cdot (\overline{A} + \overline{B})$$Y = A \cdot \overline{A} + A \cdot \overline{B} + B \cdot \overline{A} + B \cdot \overline{B}$Since $A \cdot \overline{A} = 0$ and $B \cdot \overline{B} = 0$,we get:$Y = A \cdot \overline{B} + B \cdot \overline{A}$This is the Boolean expression for an $XOR$ gate.

The given logic circuit is equivalent to which gate?

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