24 votes 24 votes Consider the two cascade $2$ to $1$ multiplexers as shown in the figure . The minimal sum of products form of the output $X$ is $\overline{P} \ \overline {Q}+PQR$ $\overline{P} \ {Q}+QR$ $PQ +\overline{P} \ \overline{Q}R$ $\overline{Q} \ \overline{R} + PQR$ Digital Logic gatecse-2016-set1 digital-logic multiplexer normal + – Sandeep Singh asked Feb 12, 2016 edited Feb 20, 2018 by go_editor Sandeep Singh 9.3k views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
Best answer 48 votes 48 votes 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 monanshi answered Feb 12, 2016 selected Feb 12, 2016 by Praveen Saini monanshi comment Share Follow See all 2 Comments See all 2 2 Comments reply manojkoppolu commented May 16, 2021 reply Follow Share why option A is incorrect ,option a and d are same right 0 votes 0 votes IshanBhusari commented Nov 10, 2023 reply Follow Share no they are not 0 votes 0 votes Please log in or register to add a comment.
1 votes 1 votes 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 shivam001 answered Nov 23, 2019 shivam001 comment Share Follow See all 0 reply Please log in or register to add a comment.
0 votes 0 votes 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.. Joker answered Mar 6, 2016 Joker comment Share Follow See all 0 reply Please log in or register to add a comment.
0 votes 0 votes 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. DIBAKAR MAJEE answered Apr 27, 2020 DIBAKAR MAJEE comment Share Follow See all 0 reply Please log in or register to add a comment.