GATE Overflow | Mock GATE | Test 1 | Question: 58

Question

Let $f(A, B, C, D)=\Pi (2, 3, 5, 9, 11, 12, 13)$
The total number of prime implicants and essential prime implicants are denoted by $P$ and $Q$ respectively. What is the value $Q \% P$ where $'\%'$ denotes the modulo operator?

Comments

@Ruturaj Mohanty @chauhansunil20th

http://sce2.umkc.edu/csee/hieberm/281_new/lectures/simplification/k-map-pos.html

Here they have found prime implicant(PI)  for maxterms and essential prime implicant (EPI) for maxterms. Please tell whether PI and EPI is possible $\textbf{only}$ for minterms

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Please refer standard text books instead of arbitrary google links.
https://books.google.co.in/books?id=CxEwDwAAQBAJ&pg=PA94&lpg=PA94&dq=morris+mano+prime+implicant&source=bl&ots=on1q-E2hS-&sig=wye-bVRF9T3DV3AuGbp5sZxR0UE&hl=en&sa=X&ved=2ahUKEwjZ9tT9p9zfAhVEPI8KHTNjC2cQ6AEwCXoECAoQAQ#v=onepage&q=morris%20mano%20prime%20implicant&f=false

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in SOP epi is 3 , what is difference between sop and pos regarding epi. which one shud i consider for exam ?

Answer 1

$f(A,B,C,D)=Π(2,3,5,9,11,12,13)=Σ(0,1,4,6,7,8,10,14,15) $

There are $7$ Prime implicants, among them, there are $2$ EPIs closed in green rectangles and remaining $5$ are non-essential Prime Implicants which are pointed by red arrows.

P = Prime Implicants = 7, Q = Essential Prime Implicants = 2

$\text{Q%P} = \text{2%7}=2$ Hence, 2 is the correct answer.