GATE | GATE-CS-2015 (Set 3) | Question 65

The total number of prime implicants of the function f(w, x, y, z) = Σ(0, 2, 4, 5, 6, 10) is ________.
(A) 2
(B) 3
(C) 4
(D) 5


Answer: (B)

Explanation:

Red,Blue and Green together make total three prime implicant.

As we know “A prime implicant of a function is an implicant that cannot be covered by a more general (more reduced – meaning with fewer literals) implicant. (Wikipedia)” we’ve to see only prime implicants . We can make group of four 1’s as in the figure(green group) , a group of two 1’s in blue and red .As we can’t reduce it further so this is minimal representation of problem and hence total number of prime implicant =3. So answer (B) part.

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