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A logical function is given as *F*(*A*, *B*, *C*, *D*) = Σ*m* (0, 4, 5, 10, 11, 13, 15). The number of Essential Prime Implicants in the given function will be _________.

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Essential prime implicant is basically a prime implicant , but it can cover outputs of a function which no other combination of prime implicants can cover.

1 at 0000 and at 1010 has only one possible way to be grouped , but others have two possibilities.

Thus there are only 2 essential prime implicants , which shall exist in all possible groupings of 1's at 0000 and at 1010

1 at 0000 and at 1010 has only one possible way to be grouped , but others have two possibilities.

Thus there are only 2 essential prime implicants , which shall exist in all possible groupings of 1's at 0000 and at 1010

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https://gateoverflow.in/292988/madeeasy-test#c293025

See this question for reference

And you problem is not EPI or PI even in K-map you can't do this like diagonally.

EPI is also a prime implicant which have atleast 1 minterm covered by only one PI.

Every possible combination of minterms is PI.

In your case its is **6 PI** and **2 EPI **

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