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 .
Also explain the prime implicants and essential prime implicants with don't care
condition .
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
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
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
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, 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.
@Pawan I don't think so it is prime implicant. Let the question is this.
only 3 is added in Sigma part. Try it and say your answer.
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 .
I think essential prime implicant must be present in minimal expression..
Why not? @Bikram
Sir in above comment you have told that
@Bikram
$F=\Sigma(1,2,3,5,7,12)+d(0,9,13)$
3EPI and 4PI
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?
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.
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 .
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 .
