Question

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

• A. W+(X+Y)
• B. W + (X Y)
• C. W .(X . Y)
• D. W. (X + Y)

Answer 1

Answer: (B)

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 $W+Y$.

Net output is
$F=(W+X)\cdot (W+Y)$
$=W\cdot W+WY+XW+XY$
$=W+WY+XW+XY$
$=W(1+Y)+XW+XY$
$=W+WX+XY$
$=W(1+X)+XY$
$F=W+XY$