GATE CSE 2016 Set 1 | Question: 30

Question

Consider the two cascade $2$ to $1$ multiplexers as shown in the figure .

    

The minimal sum of products form of the output $X$ is 

• A. $\overline{P} \ \overline {Q}+PQR$
• B. $\overline{P} \ {Q}+QR$
• C. $PQ +\overline{P} \ \overline{Q}R$
• D. $\overline{Q} \ \overline{R} + PQR$

Answer 1

Assume P=0 and Q=0 The output should be R' Only option D satisfies this case.   Hence, D is the correct choice.

Answer 2

Output of 1st MUX is

Now 

Hence D is the answer

 

Answer 3

 

Here is my solution.