Question

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

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

Answer 1

Hint: Different gates represent different operations.
OR gate adds the input.
AND gate multiplies the input.
Fig1 depicts the problem in hand

Complete step by step solution:
Given:
1. Circuit diagram as given in circuit with inputs P, Q, R, and output A.
2. 2 OR gates and 1 AND.
To find: The expression for output A.
Step 1 of 3:
Find the out of upper OR gate, let it be X:
$X = P + R$
Find the out of lower OR gate, let it be Y:
$Y = P + Q$
Step 2 of 3:
Now X and Y are inputs to the AND gate.
$A = X \cdot Y$
Substitute the value of X and Y:
$A = (P + R) \cdot (P + Q)$
$
  A = PP + PQ + RP + RQ \\
  A = P(1 + Q) + RP + RQ \\
 $
Step 3 of 3:
We know that the AND gate applied on 1 with any other input gives 1. This implies that $(1 + Q = 1)$:
$
  A = P + R \cdot P + R \cdot Q \\
  A = P(1 + R) + R \cdot Q \\
 $
Again, we know that the AND gate applied on 1 with any other input gives 1. This implies that $(1 + R = 1)$:
$A = P + R \cdot Q$

The output A of the circuit is represented by $P + (R.Q)$. Hence the correct option is (C).

Note:
Logic gates are circuits made up of transistors and diodes as deciding components. It is these transistors that act as a switch, adder to the voltage signals applied through it. We commonly use RAM, in our PC, phone, etc. but all these are just a combination of flip flop logic gate circuits which enables us to store information. In questions like these, carefully look at the circuit diagram to identify the gates used. Apply proper operations corresponding to the gates.