Consider the minterm list form of a Boolean function 𝐹 given below

Q. Consider the minterm list form of a Boolean function 𝐹 given below.

𝐹(𝑃, 𝑄, 𝑅, 𝑆) = ∑ 𝑚(0, 2, 5, 7, 9, 11) + 𝑑(3, 8, 10, 12, 14)

Here, 𝑚 denotes a minterm and 𝑑 denotes a don’t care term. The number of essential prime implicants of the function 𝐹 is_______.

Ans: 3

Sol:

Essential Prime Implicants are those subcubes (groups) which cover atleast one minterm that can’t be covered by any other prime implicant. Essential prime implicants (EPI) are those prime implicants which always appear in final solution.

There are three prime implicants P’QS, PQ’ and Q’S’. Also, all of them are essential. Therefore, the number of essential prime implicants of function F is 3.