Figure gives a system of logic gates. From the study of truth table it can be found that to produce a high output (1) at R, we must have

Question

Figure gives a system of logic gates. From the study of truth table it can be found that to produce a high output (1) at R, we must have (A) X = 0, Y = 1 (B) X = 1, Y = 1 (C) X = 1, Y = 0 (D) X = 0, Y = 0

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/c68b63df3d186e3e421b316210e93914-.png" /> The truth table can be written as X Y barX barY P= barX +Y Q= overlineX barY R= overlineP+Q 0 1 1 0 1 1 0 1 1 0 0 1 1 0 1 0 0 1 0 0 1 0 0 1 1 1 1 0 Hence X=1, Y=0 gives output R=1

$X$	$Y$	$\overset{ˉ}{X}$	$\overset{ˉ}{Y}$	$P = \overset{ˉ}{X} + Y$	$Q = \overline{X \overset{ˉ}{Y}}$	$R = \overline{P + Q}$
0	1	1	0	1	1	0
1	1	0	0	1	1	0
1	0	0	1	0	0	1
0	0	1	1	1	1	0

Q. Figure gives a system of logic gates. From the study of truth table it can be found that to produce a high output (1) at $R$ , we must have

X = 0, Y = 1

X = 1, Y = 1

X = 1, Y = 0

X = 0, Y = 0

The truth table can be written as

$X$ $Y$ $\overset{ˉ}{X}$ $\overset{ˉ}{Y}$ $P = \overset{ˉ}{X} + Y$ $Q = \overline{X \overset{ˉ}{Y}}$ $R = \overline{P + Q}$

0 1 1 0 1 1 0

1 1 0 0 1 1 0

1 0 0 1 0 0 1

0 0 1 1 1 1 0

Hence $X = 1, Y = 0$ gives output $R = 1$

Q. Figure gives a system of logic gates. From the study of truth table it can be found that to produce a high output (1) at R, we must have