11 votes

for given boolean function what will b the no of prime implicants and no of essential prime implicants

F(A,B,C,D)=Σ_{m} (1,3,4,5,9,11,14,15) +d(2,6,7,8)

where d represents dont cares.

11 votes

Best answer

**EDIT : --------------- **

Besides the prime implicants mentioned above, CD and A'D will also be a prime implicant .* Hence we have 7 prime implicants in total.*.

However for being an essential prime implicant it is* "essential" *that at least one '1' is present which is not present in any other prime implicant..And in this regard "don't care terms" will not do for checking exclusiveness..Hence we need one '1' at least for a given prime implicant to be essential..

**Keeping this in mind , we have 2 essential prime implicants : a) A' B b) BC**

For reference : plz check "K Map with Dont cares" section of :

http://www-ee.ccny.cuny.edu/wwwn/yltian/Courses/EE210/EE210-Lecture7.pdf

0

Thanks I conform explenation is correct

https://math.stackexchange.com/questions/1233297/essential-prime-implicants-and-minterm-expressions

https://math.stackexchange.com/questions/1233297/essential-prime-implicants-and-minterm-expressions