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essential prime implicants

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amriths04

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function with no essential prime implicant

hi friends,
with respect to karnaugh map, what is the difference among implicants, prime implicants and essential prime implicants?

thank you in advance,
 

Hi frnd .
essential prime implicant is one which is not covered by any other square in the K map and it should be present in the simplified function...
In Boolean logic, an implicant is a "covering" (sum term or product term) of one or more minterms in a sum of products (or maxterms in a product of sums) of a boolean function.
prime implicant of a function is an implicant that cannot be covered by a more general (more reduced - meaning with fewer literals) implicant. W.V. Quine defined a prime implicant of F to be an implicant that is minimal - that is, if the removal of any literal from P results in a non-implicant for F. Essential prime implicants are prime implicants that cover an output of the function that no other prime implicant (or sum thereof) is able to cover.
 

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