GATE | GATE-CS-2004 | Question 59

Which are the essential prime implicants of the following Boolean function?
f(a, b, c) = a’c + ac’ + b’c
(A) a’c and ac’
(B) a’c and b’c
(C) a’c only
(D) ac’ and bc’

Answer: (A)

Explanation: Essential prime implicants are prime implicants that cover an output of the function that no combination of other prime implicants is able to cover i.e., if we delete such elements then the property of group, quad, octet is destroyed.

By drawing k map and by putting c on left side and a, b on right side we can find that a’c and ac’ are essential prime implicants.

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