Question

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

• A. $P\cdot (R+Q)$
• B. $P\cdot (R\cdot Q)$
• C. $P+(R\cdot Q)$
• D. $P+(R+Q)$

Answer 1

Answer: (C)

$P+(R\cdot Q)$

Output of upper OR gate $=P+R$
Output of lower OR gate$=P+Q$
$\therefore$ New output $A=(P+R)(P+Q)$
$=PP+PQ+RP+RQ$
$=P(1+Q)+RP+RQ$
$\because$ $1+Q=1$ and $PP=P$
$\therefore A=P+R\cdot P+R\cdot Q$
$=P(1+R)+R\cdot Q$ now $1+R=1$
$=P+R\cdot Q$