Question

The following configuration of gate is equivalent to :

• A. $NAND$
• B. $XOR$
• C. $OR$
• D. None of these

Answer 1

Answer: (B)

$Y=\left(A+B\right)\cdot \overline{AB}$
The given output equation can also be written as
$Y=\left(A+B\right)\cdot \left(\bar{A}+\bar{B}\right)$ (De Morgan's theorem)
$=A\bar{A}+A\bar{B}+B\bar{A}+B\bar{B}=0+A\bar{B}+\bar{A}B+0$
$=\bar{A}B+A\bar{B}$
This is the expression for $XOR$ gate.