prime implicants- essential prime implicants + (0,1) ???

11 votes

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 .`

21 votes

Best answer

**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

4

Yes, it is correct.

EPI is at position 8, 13 and 3 .

And there are only 3 EPI as we can see clearly from the diagram .

Total 5 Prime Implicants are possible .

EPI is at position 8, 13 and 3 .

And there are only 3 EPI as we can see clearly from the diagram .

Total 5 Prime Implicants are possible .

0

@Hemant Parihar, I have a doubt in the question which you posted as the first link.

In that if you see the K map of "vishwa ratna" which is the second answer, he has considered number 2 as essential PI. But the "1" at position "1001" can be covered by "X" above it and together it is a prime implicant. So how second one is essential prime implicant ?

In that if you see the K map of "vishwa ratna" which is the second answer, he has considered number 2 as essential PI. But the "1" at position "1001" can be covered by "X" above it and together it is a prime implicant. So how second one is essential prime implicant ?

2

Yes, I also think it should not be an essential prime implicant. 7 PI and 2 EPI. Let Habib confirm it. :)

0

@Hemant Parihar, According to your definition of prime implicant, if we consider all don't cares as 1's, then will a group of 4 don't cares (only don't cares) form a prime implicant? I don't think so.

1

@xylene it is not my definition, It is given the pdf link :) . Also I see few answer using this.

I also think that it should not be a prime implicants. Because we actually want to cover 1's. And we add don't care to it only when we are forming the big cube so that less literal in a term.

But I don't find any resource on it, If you find one do share :).

I also think that it should not be a prime implicants. Because we actually want to cover 1's. And we add don't care to it only when we are forming the big cube so that less literal in a term.

But I don't find any resource on it, If you find one do share :).

0 votes

prime implicantis the no. of all possible larger size subcube in k-map

essential primeimplicant 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.

1

@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.

0

yes becoz on my view to write minimal expression, essential prime implicant must present in every possible minimal expression.and u know it will be prefer over yellow marked.

correct me someone if something wrong,,,,

correct me someone if something wrong,,,,

1

@Pawan I don't think so it is prime implicant.

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.

2

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 .

1

@Bikram

Sir,

The best answer is correct, but what about the statement "every minimal expression should contain all essential prime implicants", isn't it true?

Sir,

The best answer is correct, but what about the statement "every minimal expression should contain all essential prime implicants", isn't it true?

0

essential prime implicant must present in every possible minimal expression No, EPI is not like that !

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 .

I don't think so it is prime implicant. see the best answer, it is correct .

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 .

https://gateoverflow.in/80983/no-of-essential-prime-implicants

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 .

I don't think so it is prime implicant. see the best answer, it is correct .

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 .

https://gateoverflow.in/80983/no-of-essential-prime-implicants

0

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?

0

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.

https://cse.sc.edu/~hoskinsw/classes/csce211/LecturesF15/Lecture8.pdf

https://gateoverflow.in/232643/epi-question?show=232643

http://media-lab.ccny.cuny.edu/wordpress/YLTCCNYHomepage/Courses/EE210/EE210-Lecture7.pdf

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.

5 Prime implicants and 3 Essential prime implicants.

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.

https://cse.sc.edu/~hoskinsw/classes/csce211/LecturesF15/Lecture8.pdf

https://gateoverflow.in/232643/epi-question?show=232643

http://media-lab.ccny.cuny.edu/wordpress/YLTCCNYHomepage/Courses/EE210/EE210-Lecture7.pdf

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.

5 Prime implicants and 3 Essential prime implicants.

0

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.

0

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 .

0

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 .

https://gateoverflow.in/?qa=blob&qa_blobid=5414455466690637946

Here in the image prime implicants are marked with a rectangle.

Essential prime implicants have 1*.

https://gateoverflow.in/?qa=blob&qa_blobid=5893376068232915243

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.

5 Prime implicants and 3 Essential prime implicants.....

Explain by drawing K-map.

Also explain the prime implicants and essential prime implicants with don't care condition .

https://gateoverflow.in/?qa=blob&qa_blobid=5414455466690637946

Here in the image prime implicants are marked with a rectangle.

Essential prime implicants have 1*.

https://gateoverflow.in/?qa=blob&qa_blobid=5893376068232915243

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.

5 Prime implicants and 3 Essential prime implicants.....