44 votes 44 votes The total number of prime implicants of the function $f(w, x, y, z) = \sum (0, 2, 4, 5, 6, 10)$ is __________ Digital Logic gatecse-2015-set3 digital-logic canonical-normal-form normal numerical-answers + – go_editor asked Feb 15, 2015 • edited Feb 10, 2018 by go_editor go_editor 17.5k views answer comment Share Follow See all 13 Comments See all 13 13 Comments reply Show 10 previous comments KUSHAGRA गुप्ता commented Jul 18, 2020 i moved by KUSHAGRA गुप्ता Jul 18, 2020 reply Follow Share Make use of Quine-McCluskey Method : Prime Implicants are the crossed one $(\times)$ : $m_{2}+m_{10}|m_{4}+m_{5}|m_{0}+m_{2}+m_{4}+m_{6}$ Total of 3 Prime implicants. 0 votes 0 votes Himanshu Kumar Gupta commented Aug 29, 2020 reply Follow Share answer is 3 0 votes 0 votes shashankrustagi commented Jan 11, 2021 reply Follow Share Quine-McCluskey Method : not required for GATE 3 votes 3 votes Please log in or register to add a comment.
Best answer 64 votes 64 votes As you can see that there is one $4$ -set and two $2$ -set that are covering the star marked $1's$ (i.e. the ones that are not covered by any other combinations). So, the answer is $3$. Tamojit Chatterjee answered Mar 3, 2015 • edited Apr 24, 2019 by ajaysoni1924 Tamojit Chatterjee comment Share Follow See all 13 Comments See all 13 13 Comments reply saket nandan commented Jun 30, 2015 reply Follow Share this is wrong u r saying about essential prime implecants and also EPI is 3 because where quad is formed that group must be countede as 1 so EPI is also 3 4 votes 4 votes prasitamukherjee commented Sep 14, 2016 reply Follow Share This is Essential Prime Implicants not Prime Implicants. Prime Implicants is all possible combinations right? I'm getting 6 1 votes 1 votes mcjoshi commented Sep 14, 2016 i edited by mcjoshi Sep 14, 2016 reply Follow Share No, $PI = 3$ correct. 8 votes 8 votes Pavan Kumar Munnam commented Sep 14, 2016 reply Follow Share doesn't prime implicants mean the number of product terms that come in the minimized sum of products.... correct me if i am wrong 0 votes 0 votes mcjoshi commented Sep 14, 2016 reply Follow Share No, Not necessary. Prime Implicant : the biggest subcube that should not be completely covered by any other subcube (some may be covered) Have a look my this answer. ( this can be of some help to you) 20 votes 20 votes prasitamukherjee commented Sep 14, 2016 reply Follow Share then what is the difference between PI and EPI? Here is what wiki says : As per this definition PI may have all it's outputs covered, but EPI shouldn't 2 votes 2 votes Arjun commented Sep 14, 2016 reply Follow Share @Shalini EPI are marked with * in the given answer. And question asks for no. of PI and I guess you are counting no. of distinct terms which can come in any PI. 1 votes 1 votes prasitamukherjee commented Sep 14, 2016 reply Follow Share Yes Sir. But I'm failing to understand the definition of PI. If a ques asks for num of PIs, then we should consider minimal covering of the map?(i.e. 1 subcube should not be completely covered by another subcubes, for all subcubes) 0 votes 0 votes Arjun commented Sep 14, 2016 reply Follow Share Yes, you get one minimal cover. Now, try to change this- how many changes you can do is the answer. 3 votes 3 votes Shivangi Verma commented Jan 22, 2017 reply Follow Share PI is three and Is number of essential prime implicant 2? 0 votes 0 votes Sandeep Suri commented Jan 26, 2017 reply Follow Share @shivangi EPI are term which are not covered and they are 4 marked by * 0 votes 0 votes rohan mishra commented Aug 16, 2017 reply Follow Share EPI should be 3 not 4. As we are able to cover all 1's in 3 PI. 0 votes 0 votes gari commented Aug 19, 2017 reply Follow Share I agree that no of EPI = 3 0 votes 0 votes Please log in or register to add a comment.
10 votes 10 votes (Can be solved using K-Map also. ) Place all minterms that evaluate to one in a minterm table. Input (first column for no. of 1's) 0 m0 0000 1 m2 m4 0010 0100 2 m5 m6 m10 0101 0110 1010 Combine minterms with other minterms. If two terms vary by only a single digit changing, that digit can be replaced with a dash indicating that the digit doesn't matter. Terms that can't be combined any more are marked with a "*". When going from Size 2 to Size 4, treat '-' as a third bit value. For instance, -110 and -100 or -11- can be combined, but -110 and 011- cannot. (Trick: Match up the '-' first.) First Comparison 0 (2, 0) (4, 0) 00-0 0-00 1 (6, 2) (10, 2) (5, 4) (6, 4) 0-10 -010 010- 01-0 Second Comparison 0 (6, 4, 2, 0) 0--0 Prime Implicants (6, 4, 2, 0) 0--0 (10, 2) (5, 4) -010 010- Answer: Total number of prime implicants Source: Finding prime implicants - Quine-McCluskey algorithm - Wikipedia Shyam Singh answered Feb 19, 2015 Shyam Singh comment Share Follow See all 2 Comments See all 2 2 Comments reply Nitesh Choudhary commented Jul 20, 2017 reply Follow Share is Quine McCluckey algo in gate syllabus 2 votes 2 votes mahendrapatel commented Jan 27, 2023 reply Follow Share na ,not in syllabus 0 votes 0 votes Please log in or register to add a comment.
7 votes 7 votes all the min terms can only be covered by three diffrernt color so there is only three prime imlecants saket nandan answered Jun 30, 2015 saket nandan comment Share Follow See all 0 reply Please log in or register to add a comment.
3 votes 3 votes I think this is bit easier to understand. The hint here is that we try to find the minimum number of groups(octa(eight 1's) ,quad (four 1's),dual(two 1's) that can be formed and that represents the minimum number of implicants that covers F which is Prime Implicant. Here, we can form 1 quad and 2 duets.3 prime implicants. Ayush Upadhyaya answered Jan 26, 2017 • edited Jul 20, 2018 by Ayush Upadhyaya Ayush Upadhyaya comment Share Follow See all 2 Comments See all 2 2 Comments reply Harsh Kumar commented Jul 19, 2018 reply Follow Share The blue combination is wrong. There is two bits of difference between the blue combination. 1 votes 1 votes Ayush Upadhyaya commented Jul 20, 2018 i edited by Ayush Upadhyaya Jul 20, 2018 reply Follow Share @Harsh Kumar-Yes, this is wrong. Thanks :) Corrected Now. Please verify. 0 votes 0 votes Please log in or register to add a comment.