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

For $2 :1$ MUX, output $Y=S'I_o+SI_1$

So, output of MUX$1$ ,$f_1=P'0+PR =PR$

Output of MUX$2$ , $f_2=Q'R'+Qf_1=Q'R'+PQR$

which is option D

Comments

why option A is incorrect ,option a and d are same right

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no they are not

Answer 2

Answer : D

Lets say output of 1st  multiplexer = m

table for 1st multiplexer

P	m
0	0
1	R

m = (P' * 0) + (P * R ) = PR ...(1)

table for 2nd multiplexer

Q	X
0	R'
1	m

X = (Q' * R') + (Q * m) ...(2)

put (1) in (2)

X=(Q' * R') + (Q * PR)

X= Q' R'+PQR

 

Answer 3

Let the output of 1st mux be S

S=P'.0+PR=>PR

now the 2nd Mux would give the output =>

Q'R'+QPR

so option D is the right answer..

Answer 4

the output of the first MUX is Y= PR+P' 0=PR and this will input for the second mux as these are cascaded.

for the second mask   output=PRQ+Q'R' which is the option D.