25 votes 25 votes The minterm expansion of $f(P,Q,R) = PQ +Q \bar{R}+P\bar{R}$ is $m_2+m_4+m_6+m_7$ $m_0+m_1+m_3+m_5$ $m_0+m_1+m_6+m_7$ $m_2+m_3+m_4+m_5$ Digital Logic gatecse-2010 digital-logic canonical-normal-form normal + – go_editor asked Sep 29, 2014 edited Oct 25, 2016 by go_editor go_editor 7.3k views answer comment Share Follow See all 2 Comments See all 2 2 Comments reply mohan123 commented Nov 6, 2019 reply Follow Share order of function P R Q weight of P=4,Q=2,R=1) absent variable we can take 0 and 1 both possibility total possible no PQ=(1110,111)=6,7 QR'=(010,110)=2,6 PR'=(100,110)=4,6 so min term (2,4,6,7) option A 0 votes 0 votes Himanshu Kumar Gupta commented Aug 29, 2020 reply Follow Share i think option A is right 0 votes 0 votes Please log in or register to add a comment.
Best answer 42 votes 42 votes $PQ + QR' + PR' = PQR + PQR' + PQR' + P'QR' + PQR' + PQ'R' $ $\quad= PQR + PQR' + P'QR' + PQ'R' (111 + 110 + 010 + 100)$ $\quad =m_7 + m_6 + m_2 + m_4$ Option A. Alternatively, Using K-map Arjun answered Nov 7, 2014 edited Apr 24, 2019 by ajaysoni1924 Arjun comment Share Follow See all 6 Comments See all 6 6 Comments reply Show 3 previous comments Lakshman Bhaiya commented Oct 13, 2018 reply Follow Share @raushan sah You can expand all the term $f(P, Q, R)=PQ+Q\bar{R}+P\bar{R}$ $f(P, Q, R)=PQ(R+\bar{R})+(P+\bar{P})Q\bar{R}+P(Q+\bar{Q})\bar{R}$ $f(P, Q, R)=PQR+PQ\bar{R}+PQ\bar{R}+\bar{P}Q\bar{R}+PQ\bar{R}+P\bar{Q}\bar{R}$ $f(P, Q, R)=PQR+PQ\bar{R}+\bar{P}Q\bar{R}+P\bar{Q}\bar{R}$ [Remove the similar term] In case of Sum of Product,we all know variable represent value $'1'$ and complement of variable represent the value $'0'.$ $f(P, Q, R)=PQR(111)+PQ\bar{R}(110)+\bar{P}Q\bar{R}(010)+P\bar{Q}\bar{R}(100)$ We can also represent,these minterm as $f(P, Q, R)=\sum(7,6,4,2)$ and $m_{2}+m_{4}+m_{6}+m_{7}$ is also correct. [Because we write sum of min-term=sum of product term(Canonical)] 4 votes 4 votes raushan sah commented Oct 13, 2018 reply Follow Share @lakshman thanx yes got it 1 votes 1 votes talha hashim commented Nov 5, 2018 reply Follow Share nice @arjun sir 0 votes 0 votes Please log in or register to add a comment.
5 votes 5 votes option A =PQ(R+~R)+(P+~P)Q~R+P~R(Q+~Q) on simplification we will get minterms as 2,4,6,7 saipriyab answered Nov 5, 2017 saipriyab comment Share Follow See all 0 reply Please log in or register to add a comment.
3 votes 3 votes Answer: OPTION A vannjot answered Sep 23, 2019 vannjot comment Share Follow See all 0 reply Please log in or register to add a comment.