15 votes 15 votes The simplified SOP (Sum of Product) from the Boolean expression $$(\text{P} + \overline{\text{Q}} + \overline{\text{R}}) . (\text{P} + \text{Q + R) . (P + Q} +\overline{\text{R}})$$ is $(\overline{\text{P}}.\text{Q}+\overline{\text{R}})$ $(\text{P + Q}.\overline{\text{R}})$ $(\text{P}.\overline{\text{Q}}+\text{R})$ $\text{(P.Q + R)}$ Digital Logic digital-logic canonical-normal-form isro2016 + – Arjun asked Jul 4, 2016 • edited Dec 7, 2022 by Lakshman Bhaiya Arjun 8.3k views answer comment Share Follow See 1 comment See all 1 1 comment reply Himanshu Kumar Gupta commented Aug 29, 2020 reply Follow Share i think B is right Answer 0 votes 0 votes Please log in or register to add a comment.
Best answer 18 votes 18 votes $(P + \bar{Q} + \bar{R}) . (P + {Q} + R) . (P + Q +\bar{R})$ $(P + \bar{Q} + \bar{R}) . (P +(Q+R)(Q+\bar{R}))$ $(P + \bar{Q} + \bar{R}) . (P + Q)$ $(P + (\bar{Q}+ \bar{R})Q)$ $P+Q \bar{R}$ Hence,option(B)$P+Q \bar{R}$ is the correct choice. LeenSharma answered Jul 4, 2016 • edited Jul 4, 2016 by LeenSharma LeenSharma comment Share Follow See all 0 reply Please log in or register to add a comment.
13 votes 13 votes ans is B (p+q'+r')(p+q+r)(p+q+r')=(p+q'+r')(p+q) (since a=(a+b)(a+b') so putting p+q as a here) =(p+q')(p+q) +(p+q)r' =p+pr'+qr'=p(1+r')+qr'=p+qr' (again using above law and 1+anything=1 Sanjay Sharma answered Jul 4, 2016 Sanjay Sharma comment Share Follow See all 0 reply Please log in or register to add a comment.
8 votes 8 votes Answer is (B) part. Another way to solve this problem is as follow --> Chhotu answered Apr 23, 2017 Chhotu comment Share Follow See all 2 Comments See all 2 2 Comments reply Mk Utkarsh commented Apr 27, 2018 reply Follow Share 0,1 and 3 should be filled with 0 right? 1 votes 1 votes abhishekmehta4u commented Apr 27, 2018 reply Follow Share yes 0,1 and 3 must be 0. 0 votes 0 votes Please log in or register to add a comment.
7 votes 7 votes (P+Q'+R').(P+Q+R).(P+Q+R') is Standard POS which is eqt to ∐ (0,1,3) . So Standard SOP =∑(2,4,5,6,7) when we simplified by K-Map it will gives (P+QR'). Hence (B) (P+QR') is Correct option. Warrior answered May 1, 2017 Warrior comment Share Follow See 1 comment See all 1 1 comment reply shweta1920 commented Aug 25, 2017 reply Follow Share thank you ... 0 votes 0 votes Please log in or register to add a comment.