PI and EPI in case of Don't care

Question

Consider the below function

$f=\sum m(0,1,2,5,8,15)+d(6,7,10)$

In this Prime Implicant count comes-7 and Essential Prime Implicant Count comes 2.

Please verify.

Comments

1,5 is not a epi, because there is no '1' which can't be combined in other way..

(I am not receiving emails notification for comments :(

---

@Verma Ashish
 

That's the correct explanation.

---

Thanks, @Verma Ashish @techbd123

Answer 1

Everything that I concluded-

 

Please correct me if I am wrong somewhere.

Comments

mam, i have a basic doubt that

Why can't you form sub-cube with 0's

---

If I form subcubes of 0's also then nothing will be left. ?

---

i mean, for f(x,y,z) = ∑ (0,1) + ∅ (2,6)

if we form sub cubes for zero's====> we are getting only 2 right ?

---

Why are you forming subcubes of 0's ?

---

function can be represent by pos form also... i want to go in that way... what's wrong in that?

---

Yeah. In that case we will get 3 by f1 right ?

---

but i am getting only 2...

1) 100,101,111,110

2) 011,010,111,110

---

Yes, in pos it's 2. But Is it necessary to have equal no. of PIs in Sop as well as pos.?

It's not ..

---

Then my question arises that is it 2 or 3, because in the question they didn't mention it is sop or pos

---

It's SOP and 3 PIs

---

@Shaik Masthan , In the given question , it is mentioned sigma sign . So , we have to take minterms and make switching expression in sop form. If it is pi sign, then we will take maxterms and form switching expression in pos

---

@Shaik . Here is a nice question for you -
 

Now tell us the number of PIs here.
And their minterms and expression too. 

---

mam, i doesn't ask that question

Then my question arises that is it 2 or 3, because in the question they didn't mention it is sop or pos

not only for this question, it applicable to  your above example also... i mean i asked that in general.

 

@ankitgupta.1729, Brother why not question convert in to pi symbol?

---

@ankitgupta.1729, they are asking about EPI's... in ∑ to ∏ also i am getting 3 only.

---

@Soumya-The answer to the question that you given to shaik

Number of PI are 3 $[xz(E),wz,w\lnot x(E)]$

Essential PI are indicated by (E)

minimal form=$xz+w\lnot x$

is answer correct?

---

I have one doubt. Definition of implicant is that if it is true then function must be true. Then if we consider that all x's can be combined to give prime implicant but does that prime implicant implies function?