Digital Logic, Essential Prime Implicants

Question

The number of essential prime implicants in the function f(a, b, c, d) = Σ(1, 2, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15) is ________.

Comments

https://gateoverflow.in/168324/essential-prime-implicants

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Ans 3 ?

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As all the 1’s have morethan 1 group so no of EPI=0

Answer 1

First, convert the expression given into Karnaugh map.

Given $f(a, b, c, d) = Σ(1, 2, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15)$. Corresponding Karnaugh map is:

1. Prime Implicants: A group of squares or rectangles made up of a bunch of adjacent minterms which is allowed by the definition of K-Map are called prime implicants(PI) i.e. all possible groups formed in K-Map. 

2. Essential Prime Implicants: These are those subcubes(groups) that cover at least one minterm that can’t be covered by any other prime implicant. Essential prime implicants(EPI) are those prime implicants that always appear in the final solution. 

3. Redundant Prime Implicants: The prime implicants for which each of its minterm is covered by some essential prime implicant are redundant prime implicants(RPI). This prime implicant never appears in the final solution. 

4. Selective Prime Implicants: The prime implicants for which are neither essential nor redundant prime implicants are called selective prime implicants(SPI). These are also known as non-essential prime implicants. They may appear in some solution or may not appear in some solution. 

Here, we need to find the $EPI$s, so group the squares (although a bit ambiguous here).

All the squares in all the groupings are covered by more than one prime implicant. So the number of Essential Prime Implicants is $0$.

 

Answer 2

if we draw the k map and check for  the pis we will get 0 epi.
so we need to draw first the kmap.
and then we need to marks all the prime implicants.
we will not be able to find any prime implicate member alone here so there is 0 EPI