Question

For an n-variable Boolean function, the maximum number of prime implicants are

A. 2(ⁿ⁻¹)
B. n/2
C. 2ⁿ
D. 2(ⁿ⁻¹)

Answer 1

The maximum number of prime implicants for an n-variable Boolean function is 2^(n-1).

Step-by-step explanation:

The maximum number of prime implicants for an n-variable Boolean function is represented by option D, which is 2(n-1).

To understand why this is the correct answer, let's break down the concept of prime implicants. A prime implicant is a product term in the Boolean function that covers at least one minterm or row in the truth table, and cannot be further reduced or combined with other prime implicants.

For an n-variable Boolean function, each minterm can be represented by a product term, and there can be a maximum of 2n minterms. Therefore, the maximum number of prime implicants is also 2n. However, since we need to account for the fact that some prime implicants can overlap and cover the same minterms, the actual maximum number of prime implicants is 2(n-1).