question_answer

The diagram of a logic circuit is given below The output F of the circuit is represented by:

A) W + (X + V)                        

B) W + (X Y)

C) W. (X . Y)                             

D)  W. (X + Y)

Correct Answer: B

Solution :

The circuit consists of 2 OR gates and 1 AND gate. Output of upper OR gate is W + X. Output of lower OR gate is W + V. Net output is \[F=(W+X).(W+Y)\] \[=W.W+WY+XW+XY\] \[=W+WY+XW+XY\] \[=W(1+Y)+XW+XY\] \[=W+WX+XY\] \[=W(1+X)+XY\] \[F=W+XY\]