question_answer

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

Correct Answer: C

Solution :

The truth table can be written as

X	Y	\[\bar{X}\]	\[\bar{Y}\]	\[P=\bar{X}+Y\]	\[Q=\overline{X.\bar{Y}}\]	\[R=\overline{P+Q}\]
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