question_answer

The following configuration of gate is equivalent to

A) \[NAND\]                           

B) \[XOR\]

C) \[OR\]                                  

D)  none of these

Correct Answer: B

Solution :

\[Y=(A+B)\cdot \overline{AB}\] The given output equation can also be written as \[Y=(A+B)\cdot (\bar{A}+\bar{B})\]                                             (De Morgans theorem) \[=A\bar{A}+A\bar{B}+B\bar{A}+B\bar{B}\] \[=0+A\bar{B}+A\bar{B}+0=\bar{A}B+A\bar{B}\] This is the expression for XOR gate.