36 36 votes The boolean function for a combinational circuit with four inputs is represented by the following Karnaugh map. Which of the product terms given below is an essential prime implicant of the function? $\text{QRS}$ $\text{PQS}$ $\text{PQ'S'}$ $\text{Q'S'}$ Digital Logic gateit-2006 digital-logic k-map normal + – Ishrat Jahan 10.5k views answer comment Share Follow Print See all 4 Comments 4 4 Comments reply Prateek kumar commented Sep 16, 2016 i edited by Lakshman Bhaiya Oct 14, 2019 reply Follow flag Total number of PI =7 Total number of EPI=1 //which match to all corners 1's =Q'S' 17 17 replyShare Chhotu commented Dec 28, 2017 i edited by Chhotu Dec 28, 2017 reply Follow flag https://math.stackexchange.com/questions/20915/question-on-essential-prime-implicants https://gateoverflow.in/138655/prime-implicants-and-essential-prime-impliccants https://gateoverflow.in/80983/no-of-essential-prime-implicants 0 0 replyShare svas7246 commented Jul 23, 2022 reply Follow flag Don't fall in the trap and take pq’s’ as the answer in the corners you need to take the biggest sub cube possible 0 0 replyShare GO Classes commented Jun 22 reply Follow flag Watch Solution here! 1 1 replyShare Please log in or register to add a comment.
Best answer 45 45 votes Only the top leftmost and bottom rightmost $1s$ have no alternate groupings. So, they form the essential prime implicants. Answer is D. $Q'S'$ Ankit pipaliya answered Nov 30, 2017 • selected Apr 26, 2019 by Arjun Ankit pipaliya comment Share Follow See all 7 Comments 7 7 Comments reply Show 4 previous comments Abhrajyoti00 commented Jan 5, 2023 reply Follow flag # $EPI = 1 (Q’S’)$ # $PI = 7$ 7 7 replyShare Hira Thakur commented Nov 1, 2023 reply Follow flag how many redundant EPI and selective EPI are here??? 0 0 replyShare sru12 commented Jun 10, 2024 reply Follow flag so are you saying that even if it is not mentioned that we need to take minimal sop then also we have to take biggest possible subcube for every minterm as in question it is not mentioned that we need to take minimal sop or pos so maybe cant we say that we can cover all the corner 1's in two ways (subcube of size 2 and size 4) is it not like if there was a minterm which only can be covered by one implicant then its essential PI ?? like even if we should take biggest possible subcube still all corner 1s can be covered in two or more ways (I would not have raised this doubt if minimal sop has mentioned in question) 0 0 replyShare Please log in or register to add a comment.
18 18 votes Essential prime implicants which $r$ grouped only by only one method or way, So, in above question cornor's ones r grouped by only one method, d ) will be the answer. saket nandan answered Jun 16, 2015 • edited Jun 26, 2018 by Milicevic3306 saket nandan comment Share Follow See 1 comment 1 1 comment reply cprdereddyy commented Sep 30, 2024 reply Follow flag why should we consider Minimal SOP 1 1 replyShare Please log in or register to add a comment.
