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+28 votes
The total number of prime implicants of the function $f(w, x, y, z) = \sum (0, 2, 4, 5, 6, 10)$ is __________
in Digital Logic by Veteran (105k points)
edited by | 3.9k views
prime implicant means?
Please explain Implicant,Prime Implicant,Essential Prime Implicant

refer here.

There are $3 \ PIs$ and all these $3$ $PIs$ are $EPIs$.




EP=3 ?

Yes you are right


@Lakshman Patel RJIT

I think EPI = 4, and not 3. You can refer the Answer, where * denotes EPI.



No, EPI$=3$, because there two-star from the same group. 


8 Answers

+43 votes
Best answer

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 $3$.

by Active (2.3k points)
edited by
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
This is Essential Prime Implicants not Prime Implicants.

Prime Implicants is all possible combinations right? I'm getting 6
No, $PI = 3$ correct.
doesn't prime implicants mean the number of product terms that come in the minimized sum of products....

correct me if i am wrong

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)


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

@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.
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)
Yes, you get one minimal cover. Now, try to change this- how many changes you can do is the answer.
PI is three and Is number of essential prime implicant 2?
@shivangi EPI are term which are not covered and they are 4 marked by *
EPI should be 3 not 4.

As we are able to cover all 1's in 3 PI.
I agree that no of EPI = 3
+8 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)

m0 0000
1 m2
2 m5

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)
1 (6, 2)
(10, 2)
(5, 4)
(6, 4)

Second Comparison

0 (6, 4, 2, 0) 0--0

Prime Implicants

(6, 4, 2, 0) 0--0
(10, 2)
(5, 4)

Answer: Total number of prime implicants 3

Source: Finding prime implicants - Quine-McCluskey algorithm - Wikipedia

by Active (1.6k points)
is Quine McCluckey algo in gate syllabus
+6 votes

all the min terms can only be covered by three diffrernt color so there is only three prime imlecants

by Active (5.1k points)
+2 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.


by Boss (27.8k points)
edited by
The blue combination is wrong. There is two bits of difference between the blue combination.
@Harsh Kumar-Yes, this is wrong. Thanks :)

Corrected Now. Please verify.
+1 vote
prime implicants are 3;

definition of prime implicant:- This is a group which is not a subset of a bigger size group.
by Active (2.3k points)
0 votes
Ans: 3
by Active (1.2k points)
0 votes

3 epi and 3 pi is possible

by Boss (35.7k points)
0 votes
every subcube is prime implicant ........ and atleast one term which is not covered by other but is only covered by prime implicant is called essential prime implecents
by (11 points)

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