Question

Determine the number of essential prime implicants of the function f(a, b, c, d) = Σm(1, 3, 4, 8, 10, 13) + d(2, 5, 7, 12), where m denote the minterm and d denotes the don’t care condition.

(a) 2^3

(b) 3

(c) 643

(d) 128

The question was asked in exam.

I want to ask this question from Boolean Algebra in division Boolean Algebra and Modeling Computations of Discrete Mathematics

Answer 1

Right option is (b) 3

To elaborate: A prime implicant that cannot be replaced by any other implicant for getting the output is called the essential prime implicants. Here, we have 3 essential prime implicants by using the K-map representation.