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 Show 6 previous comments 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 Hemant Parihar commented Jul 19, 2017 reply Follow Share @pawan, I have a doubt? Are you sure this is essential prime implicant because here there is no 1 which is not covered by any other prime implicant? We don't care about X (don't care). I agree that it will be preferred over the yellow marked prime implement because it has less literal. 1 votes 1 votes abhishekmehta4u commented Jul 19, 2017 reply Follow Share I think (0,1) is not Prime emplicant. 0 votes 0 votes pawan kumarln commented Jul 19, 2017 reply Follow Share yes becoz on my view to write minimal expression, essential prime implicant must present in every possible minimal expression.and u know it will be prefer over yellow marked. correct me someone if something wrong,,,, 0 votes 0 votes Hemant Parihar commented Jul 19, 2017 reply Follow Share @Pawan I don't think so it is prime implicant. 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. 1 votes 1 votes Bikram commented Jul 25, 2017 reply Follow Share essential prime implicant must present in every possible minimal expression No, EPI is not like that ! @pawan An essential prime implicant is a prime implicant that covers at least one 1 which does not covered by any other prime implicant . So at position 13, 8,3 have EPI . see the best answer, it is correct . 2 votes 2 votes pawan kumarln commented Jul 25, 2017 reply Follow Share thanks for pointing my mistake ..... 0 votes 0 votes Gaurav Parashar commented Aug 12, 2018 reply Follow Share @Bikram Sir, The best answer is correct, but what about the statement "every minimal expression should contain all essential prime implicants", isn't it true? 1 votes 1 votes Verma Ashish commented Jun 25, 2019 reply Follow Share I think essential prime implicant must be present in minimal expression.. Why not? @Bikram 0 votes 0 votes Bikram commented Jun 27, 2019 reply Follow Share Why not ... 0 votes 0 votes Verma Ashish commented Jun 27, 2019 reply Follow Share Sir in above comment you have told that No, EPI is not like that ! 0 votes 0 votes Bikram commented Jun 29, 2019 i edited by Bikram Jun 29, 2019 reply Follow Share essential prime implicant must present in every possible minimal expression No, EPI is not like that ! An essential prime implicant is a prime implicant that covers at least one 1 which does not covered by any other prime implicant . So at position 13, 8,3 have EPI . I don't think so it is prime implicant. see the best answer, it is correct . 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 . https://gateoverflow.in/80983/no-of-essential-prime-implicants 0 votes 0 votes Verma Ashish commented Jun 29, 2019 reply Follow Share @Bikram $F=\Sigma(1,2,3,5,7,12)+d(0,9,13)$ 3EPI and 4PI –1 votes –1 votes Verma Ashish commented Jun 29, 2019 reply Follow Share Sir, i don't have any doubt in calculating PI and EPI and yes this answer is not correct and selected one is right.. But, I was asking that- if there are some EPIs present then they all must be present in minimal expression along with some necessary prime implicant. Because if we exclude any epi then the 'atleast one 1 which is not covered by any other prime implicant' is missed from our expression. Correct? 0 votes 0 votes Bikram commented Jun 30, 2019 reply Follow Share https://gateoverflow.in/?qa=blob&qa_blobid=5414455466690637946 0 votes 0 votes Bikram commented Jul 2, 2019 i edited by Bikram Jul 2, 2019 reply Follow Share 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. https://cse.sc.edu/~hoskinsw/classes/csce211/LecturesF15/Lecture8.pdf https://gateoverflow.in/232643/epi-question?show=232643 http://media-lab.ccny.cuny.edu/wordpress/YLTCCNYHomepage/Courses/EE210/EE210-Lecture7.pdf 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. 5 Prime implicants and 3 Essential prime implicants. 1 votes 1 votes 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.