First slide

Boolean operation

Question

The following configuration of gate is equivalent to

Moderate

A

NAND
B

XOR
C

OR
D

AND

Solution

Output of $G_{1} = (A + B);$ Output of $G_{2} = \bar{A . B} = A + B$

$\begin{array}{l} Output of G_{3} = (A + B) . \bar{(A . B)} = (A + B) . (\bar{A} + \bar{B}) (∵ \bar{A . B} = \bar{A} + \bar{B}) \\ = A . \bar{A} + A . \bar{B} + B . \bar{A} + B . \bar{B} \\ = 0 + A . \bar{B} + B . \bar{A} + 0 \\ = A . \bar{B} + B . \bar{A} \end{array}$
which gives XOR gate.
Output of XOR gate is $A . \bar{B} + \bar{A} . B$
Therefore, the correct answer is (B).

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