Question

Design a logic circuit to take input signals P, Q, and R and output a 1 if , and only if, P and Q have the same value and Q and R have opposite values.

Answer 1

Step-by-step explanation:

We have 3 given inputs namely P, Q, R and we have to draw a logic circuit which will give the output 1 if , and only if, P and Q have the same value and Q and R have opposite values.

So, first of all we make a truth table for this

P        Q        R        Output(Y)

0        0        0           0

0        0         1           1

0         1        0           0

0         1         1           0

1         0        0          0

1          0        1           0

1          1        0           1

1          1         1           0    

From the truth table we can see that the output, Y can be given by

$Y=\bar{P}\bar{Q}R+PQ\bar{R}$

So, the logic circuit for the given logic equation can be drawn as shown fig.