14 votes 14 votes What are the prime implicants and essential prime implicants for the below questions ? F(w, x, y, z) = ∑(1,2,5,7,12) + d(0,9,13) Explain by drawing K-map. Also explain the prime implicants and essential prime implicants with don't care condition . Digital Logic digital-logic prime-implicants + – Kuldeep Pal asked Jul 19, 2017 retagged Aug 4, 2017 by Arjun Kuldeep Pal 20.3k views answer comment Share Follow See all 3 Comments See all 3 3 Comments reply joshi_nitish commented Jul 19, 2017 reply Follow Share essential prime inplicant- (5,7) (0,2) (12,13) (1,5,9,13) prime implicants- essential prime implicants + (0,1) ??? 3 votes 3 votes Raj Bopche commented May 19, 2021 reply Follow Share (1,5,9,13) is not an EPI, because term 13th is a don’t care term and hence cannot be considered. 0 votes 0 votes thewolf commented Jan 28, 2022 reply Follow Share @joshi_nitish Yes, thats the correct ans 0 votes 0 votes Please log in or register to add a comment.
Best answer 30 votes 30 votes K Map's with don't cares A prime implicant is a rectangle of 1, 2, 4, 8, … 1’s or X’s not included in any one larger rectangle. Thus, from the point of view of finding prime implicants, X’s (don’t cares) are treated as 1’s. An essential prime implicant is a prime implicant that covers at least one 1 not covered by any other prime implicant (as always). Don’t cares (X’s) do not make a prime implicant essential. Here in the image prime implicants are marked with a rectangle. Essential prime implicants have 1*. This blue rectangle is not essential prime implicant because here there is no 1 which is only covered by single prime implicant. There is don't care(X) which is only covered by blue rectangle but in essential prime implicant, we only want a 1 which is not covered by another prime implicant. Answer: 5 Prime implicants and 3 Essential prime implicants. Good reads. https://gateoverflow.in/80983/no-of-essential-prime-implicants http://www-ee.ccny.cuny.edu/wwwn/yltian/Courses/EE210/EE210-Lecture7.pdf Hemant Parihar answered Jul 21, 2017 selected Jul 24, 2017 by Aman Vats Hemant Parihar comment Share Follow See all 9 Comments See all 9 9 Comments reply Bikram commented Jul 25, 2017 i edited by Bikram Jul 26, 2017 reply Follow Share Yes, it is correct. EPI is at position 8, 13 and 3 . And there are only 3 EPI as we can see clearly from the diagram . Total 5 Prime Implicants are possible . 5 votes 5 votes Xylene commented Sep 13, 2017 reply Follow Share @Hemant Parihar, I have a doubt in the question which you posted as the first link. In that if you see the K map of "vishwa ratna" which is the second answer, he has considered number 2 as essential PI. But the "1" at position "1001" can be covered by "X" above it and together it is a prime implicant. So how second one is essential prime implicant ? 0 votes 0 votes Hemant Parihar commented Sep 13, 2017 reply Follow Share Yes, I also think it should not be an essential prime implicant. 7 PI and 2 EPI. Let Habib confirm it. :) 2 votes 2 votes Xylene commented Sep 13, 2017 reply Follow Share @Hemant Parihar, According to your definition of prime implicant, if we consider all don't cares as 1's, then will a group of 4 don't cares (only don't cares) form a prime implicant? I don't think so. 0 votes 0 votes Hemant Parihar commented Sep 13, 2017 reply Follow Share @xylene it is not my definition, It is given the pdf link :) . Also I see few answer using this. I also think that it should not be a prime implicants. Because we actually want to cover 1's. And we add don't care to it only when we are forming the big cube so that less literal in a term. But I don't find any resource on it, If you find one do share :). 1 votes 1 votes Xylene commented Sep 14, 2017 reply Follow Share @Hemant Parihar, Can you please share the link where they have actually used don't cares like that ? I have not seen it anywhere till now. Even in the pdf link there is no example showing this. 0 votes 0 votes Habibkhan commented Sep 14, 2017 reply Follow Share Done @Hemant..:) .. 1 votes 1 votes Waferio commented Sep 2, 2018 reply Follow Share If the only one don't care is left in a group then it is considered as the PI or not ...See the last answer given by shruthi , at position 10 01 there is a don't care , so tell me it is EPI or PI 0 votes 0 votes thewolf commented Jan 28, 2022 reply Follow Share I don’t feel this answer is correct. EPI : 4 seems correct. 0 votes 0 votes Please log in or register to add a comment.
0 votes 0 votes prime implicant is the no. of all possible larger size subcube in k-map essential prime implicant is the no. of larger size subcube which at least one cell without overlapping here red one define E.P.I. and red and yellow combined shows P.I. pawan kumarln answered Jul 19, 2017 pawan kumarln comment Share Follow See all 18 Comments See all 18 18 Comments reply Show 15 previous comments Verma Ashish commented Jul 2, 2019 reply Follow Share What's wrong in this- I don't found any error in this.. It is for $F=\Sigma(1,2,3,5,7,12)+d(0,9,13)$ Only $I,II,III$ are EPI and 4th group is considered as PI. 0 votes 0 votes Verma Ashish commented Jul 2, 2019 reply Follow Share 5 Prime implicants and 3 Essential prime implicants Right for actual question.. But that (image in above comment) is other function).. it is just reply to your comment-- Let the question is this. F(w, x, y, z) = ∑(1,2, 3, 5,7,12) + d(0,9,13) only 3 is added in Sigma part. Try it and say your answer . 0 votes 0 votes Bikram commented Jul 6, 2019 i edited by Bikram Jul 6, 2019 reply Follow Share F(w, x, y, z) = ∑(1,2,5,7,12) + d(0,9,13) Explain by drawing K-map. Also explain the prime implicants and essential prime implicants with don't care condition . https://gateoverflow.in/?qa=blob&qa_blobid=5414455466690637946 Here in the image prime implicants are marked with a rectangle. Essential prime implicants have 1*. https://gateoverflow.in/?qa=blob&qa_blobid=5893376068232915243 This blue rectangle is not essential prime implicant because here there is no 1 which is only covered by single prime implicant. There is don't care(X) which is only covered by blue rectangle but in essential prime implicant, we only want a 1 which is not covered by another prime implicant. 5 Prime implicants and 3 Essential prime implicants..... 0 votes 0 votes Please log in or register to add a comment.