Question

uestion Completion Status QUESTION 1 What are the essential prime implicants for the logic function fa,b,c,d) □ blcd Σ m(2,3,5,6,7, 10, 11, 13, 14)? labd □cid lac QUESTION 2 A minimum cost SOP cover will include? O Some of the essential prime implicants O Only the essential prime implicants O All of the essential prime implicants Clich Save and Submit to save and submit Click Save All Answers to save all answers

Answer 1

1. In order to find essential prime implicants, we have to first draw the K-map with 4 variables for the above min-terms and those min-terms which will be covered by single term, then that single min-terms will be part of essential prime implicant for the logic function f. W

Below is the K-map with 4 variable and instead of writing 1 for the min-terms, we have written them in decimal for better explanation.

0 3-フ 5一ろ

If we analyse the K-map, min-term 14 can only be covered by taking the terms (2,6,14,10) together and no other term which could cover 4 min-terms will be able to cover 14, hence the terms corresponding to (2,6,14,10) which is is essential prime implicant.

Then to cover min-terms 11, there is only one term with 4 elements would be able to cover 11 which also cover (2,3,10,11) and hence the term corresponding to it is and hence it is essential prime implicant.

Then in order to cover min-term 13, there is only one term with 2 elements would be able to cover 13 which also cover 5 and hence the term corresponding to (5,13) is and hence it is essential prime implicant.

Then to cover 7, only square of size 4 available is covering element (3,2,6,7) and the term corresponding to it is and hence it is also essential prime implicant.

So among the given 5 options, the essential prime implicants are , and . So option 2,4 and 5 are correct.

2. Minimum cost SOP cover will include all the essential prime implicants. Hence the option c is correct.

Please comment for any clarification.