Digital electronics : Essential prime implicant

Question

 Is it Right .
This is Tha case PI and EPI with don't care

Comments

@gaurav

No, there are total 5 PI is possible.. and Minimum 4 PI is possible..

question asks how many PI is there so it always be 5 , no one say minimum is 4 if it not mention explicitly !!

The P.I. w'x'y' is wrong as the "1" present at location 1 is previously covered in a bigger pair i.e. the pair of 4.

Yes it is covered priviously but we need to count it for total PI , if it says minimum then 4 is answer ..see this http://www-ee.ccny.cuny.edu/wwwn/yltian/Courses/EE210/EE210-Lecture7.pdf

can see also here https://gateoverflow.in/138655/prime-implicants-and-essential-prime-impliccants

---

Thank you @Bikram

---

@gaurav and @nitesh

actually for don't care X we can take it in any combination by taking X=1

if it is 1 [ in place of X if it is 1 given ] then only one implicant count and number of PI would be 4 then.. as PI is not part of any larger rectangle ..

hope i am clear , why here 5 is number of PI and not 4 ..

Answer 1

An essential prime implicant is a prime implicant that covers at least one 1 which does not covered by any other prime implicant .

So in your diagram at position 13, 8,3 have EPI .  Hence 3 EPI possible here .

Here total 5 Prime Implicants are there  .

And your diagram is correct.

Comments

Thanks for clearing doubt

---

What is the answer of this question

---

this question which snap you post have all wrong options given.

correct answer is 6 PI and 2 EPI .

---

Thanks sir