12 votes 12 votes Consider the below function $f=\sum m(0,1,2,5,8,15)+d(6,7,10)$ In this Prime Implicant count comes-7 and Essential Prime Implicant Count comes 2. Please verify. Digital Logic digital-logic + – Ayush Upadhyaya asked Aug 14, 2018 Ayush Upadhyaya 5.5k views answer comment Share Follow See all 38 Comments See all 38 38 Comments reply Shaik Masthan commented Aug 14, 2018 reply Follow Share i am getting 5 PI in which 2 are EPI 0 votes 0 votes arvin commented Aug 14, 2018 reply Follow Share see one will be the quad formed by considering each one from corner and rest two will be a pair(1,1) and (1,x) and one x on 6 will be left untouched because we only use it when we have any 1 to be rescued. so i am gettin 3pi 0 votes 0 votes Shaik Masthan commented Aug 14, 2018 reply Follow Share (0,2,8,10)----PI,EPI (7,15)--- PI,EPI (0,1),(1,5),(5,7) ----- PI TOTAL = 5 PI AND 2 EPI 4 votes 4 votes arvin commented Aug 14, 2018 reply Follow Share no no bro. u have missed on some point . (0,1) wont be considered and (5,7) rest everything is fine 0 votes 0 votes Shaik Masthan commented Aug 14, 2018 reply Follow Share why didn't consider (0,1) and (5,7) 0 votes 0 votes arvin commented Aug 14, 2018 reply Follow Share because it will add redundancy. 0 votes 0 votes Shaik Masthan commented Aug 14, 2018 reply Follow Share redundancy is not matter here..... i agree those are Redundtive prime implicants but PI's only 1 votes 1 votes arvin commented Aug 14, 2018 reply Follow Share Yes yes bro u right. :) 0 votes 0 votes Ayush Upadhyaya commented Aug 15, 2018 reply Follow Share I marked my PI as below In this essential ones are (I) and (V). Is it correct? 4 votes 4 votes Shaik Masthan commented Aug 15, 2018 reply Follow Share VII is should be invalid -----> due to PI should consist atleast either one minterm or one maxterm VI is a PI ------> i forget this, Thanks for correcting 0 votes 0 votes Ayush Upadhyaya commented Aug 15, 2018 reply Follow Share But you see this link https://www.ece.umd.edu/~danadach/ENEE_244_Fall_15/lec_10_notes.pdf They have considered the VII one as valid PI 2 votes 2 votes Shaik Masthan commented Aug 15, 2018 reply Follow Share may be the did mistake... VII can't a PI 1 votes 1 votes Arjun commented Aug 15, 2018 i edited by Arjun Aug 17, 2018 reply Follow Share yes, VII can not be a PI. Don't care means we have an invalid input and we just dont care what output it makes. For example, for a $3$ variable function on $x,y,z,$ say $f = 1$ for $x = 0, y = 0, z = 0$ and $x = 0, y = 0, z = 1$ is invalid (don't care). Now, for simplification of circuit, here we make the invalid input also as $1$ and thus $x = 0, y = 0$ become an implicant ($z$ omitted). But if $x = 0, y = 0, z = 0$ was also don't care, there is no need to make them $1$ - it will just make the circuit complex than minimal. That is, we make the don't cares as $1$ only if we can combine them with any minterm. Don't cares in themselves are not even implicants. Correction: As per standard reference we do include only don't cares also as prime implicants - definition of PI modified in presence of don't cares. So, VII is also a PI. 17 votes 17 votes Soumya29 commented Aug 15, 2018 reply Follow Share @Arjun sir, Block consists entirely of don't cares and is not part of a bigger block is counted as PI. I read it in 2-3 different references. :( Here also they considered it as prime implicant. It's given here in this book at page 137. It's given in Charles H. Roth too. It's the book followed by NPTEL prof.s . 9 votes 9 votes Shaik Masthan commented Aug 15, 2018 i edited by Shaik Masthan Aug 15, 2018 reply Follow Share so.... combination of don't care terms also a PI but it is redunant PI ? but i am not convinced why to add them in PI, which is un-necessary Read this Statement Any minterm with value “x” need not be covered by a prime implicant Reference http://kisi.deu.edu.tr//ozlem.karaca/LCDF4_Chap_02_P2.pdf page no.38 0 votes 0 votes srestha commented Aug 15, 2018 reply Follow Share @Soumya I think u misinterpret the line See there they 4 quad of donot care (in left) doesnot interpret as PI 0 votes 0 votes Soumya29 commented Aug 16, 2018 reply Follow Share @Shaik sir @Srestha Check this- https://electronics.stackexchange.com/questions/391206/prime-implicant/391220#391220 If still you have doubt please let me know, I can explain in detail with the help of truth table. 0 votes 0 votes srestha commented Aug 16, 2018 reply Follow Share @Soumya there is not even 1 upvote in the answer. is it reliable? 0 votes 0 votes srestha commented Aug 16, 2018 reply Follow Share here page 24 http://kisi.deu.edu.tr//ozlem.karaca/LCDF4_Chap_02_P2.pdf see all with donot care not considered 0 votes 0 votes Soumya29 commented Aug 16, 2018 reply Follow Share @Arjun sir, @Shaik sir @Srestha @Aayush. Written everything about it in the answer. Please have a look and correct me. 0 votes 0 votes srestha commented Aug 16, 2018 reply Follow Share https://ece.uwaterloo.ca/~cgebotys/NEW/223-4notes.htm 0 votes 0 votes srestha commented Aug 16, 2018 reply Follow Share @ankit see here https://en.wiktionary.org/wiki/prime_implicant it is specifically saying group of 1 or group of 0's are PI Even group of 0's also PI? but doesnot say anything about don't care 0 votes 0 votes Arjun commented Aug 17, 2018 reply Follow Share @Soumya Well, there they redefine the definition of prime implicants and as per it, we should consider only X's as also prime implicant. I'm not sure if this is standard - is missing in Morris Mano - but since standard references are having this, it is very much safe to assume the safe for GATE. But this will more likely never be asked in any standard examination :) 5 votes 5 votes Soumya29 commented Aug 18, 2018 reply Follow Share Thank you @Arjun sir verifying it. :) Sir I found this in Morris Mano supplement http://media.pearsoncmg.com/ph/esm/ecs_mano_lcdf_5/Reading_Suppliments/02_More_Optimization_supp4.pdf 5 votes 5 votes Lakshman Bhaiya commented Nov 16, 2018 i edited by Lakshman Bhaiya Nov 18, 2018 reply Follow Share $7PI$ and $2EPI$ are possible. 2 votes 2 votes Shaik Masthan commented Nov 18, 2018 reply Follow Share @Lakshman Patel RJIT did you read the discussion? minterm 6 and 7 combinely form a PI 0 votes 0 votes Lakshman Bhaiya commented Nov 18, 2018 reply Follow Share I read it but I don't know why unnecessary, take minterm $6$ and $7$(It is don't care.)? 0 votes 0 votes Shaik Masthan commented Nov 18, 2018 reply Follow Share even though it is unnecessary, you have to consider it as PI. read the commented by soumya mam 0 votes 0 votes Lakshman Bhaiya commented Nov 18, 2018 reply Follow Share It is applicable for $EPI$ also? 0 votes 0 votes Shaik Masthan commented Nov 18, 2018 reply Follow Share Actually EPI can't be formed by don't care terms 1 votes 1 votes Lakshman Bhaiya commented Nov 18, 2018 reply Follow Share Thanks I understand 0 votes 0 votes `JEET commented Dec 12, 2019 reply Follow Share @ankitgupta.1729 @Lakshman Patel RJIT @arvin Can you guys conclude this thread as you were involved in the discussion? Also, the best answer doesn't give what was asked in the question. 0 votes 0 votes `JEET commented Dec 12, 2019 reply Follow Share @techbd123 Help me out here. I am getting $\mathbf{3EPIs}$ 0 votes 0 votes `JEET commented Dec 12, 2019 reply Follow Share @Verma Ashish Why $\mathbf{1,5}$ is not an essential prime implicant? 0 votes 0 votes `JEET commented Dec 12, 2019 reply Follow Share @Verma Ashish I am still getting 3EPIs. Please help me out in this. 0 votes 0 votes Verma Ashish commented Dec 13, 2019 reply Follow Share 1,5 is not a epi, because there is no '1' which can't be combined in other way.. (I am not receiving emails notification for comments :( 3 votes 3 votes techbd123 commented Dec 13, 2019 reply Follow Share @Verma Ashish That's the correct explanation. 1 votes 1 votes `JEET commented Dec 13, 2019 reply Follow Share Thanks, @Verma Ashish @techbd123 1 votes 1 votes Please log in or register to add a comment.
Best answer 7 votes 7 votes Everything that I concluded- Please correct me if I am wrong somewhere. Soumya29 answered Aug 16, 2018 • selected Aug 18, 2018 by Shaik Masthan Soumya29 comment Share Follow See all 16 Comments See all 16 16 Comments reply Show 13 previous comments Shaik Masthan commented Aug 17, 2018 reply Follow Share @ankitgupta.1729, they are asking about EPI's... in ∑ to ∏ also i am getting 3 only. 0 votes 0 votes Ayush Upadhyaya commented Aug 22, 2018 reply Follow Share @Soumya-The answer to the question that you given to shaik Number of PI are 3 $[xz(E),wz,w\lnot x(E)]$ Essential PI are indicated by (E) minimal form=$xz+w\lnot x$ is answer correct? 3 votes 3 votes Vimal Patel commented Dec 7, 2019 reply Follow Share I have one doubt. Definition of implicant is that if it is true then function must be true. Then if we consider that all x's can be combined to give prime implicant but does that prime implicant implies function? 0 votes 0 votes Please log in or register to add a comment.