Procedure for Finding Prime Implicants

 

1)           Find prime implicants by finding all permitted (integer power of 2) maximum sized groups of min-terms.

2)           Find essential prime implicants by identifying those prime implicants that contain at least one min-term not found in any other prime implicant.

 

Example

Answer: Z

 

Rule

1)           Every variable in an Σ Π that is a 0 in every square appears complemented in the final product term.

2)           Every variable in an Σ Π that is a 1 in every square appear as is in the final product term.

3)           A 0 in half of the square a 1 in half of the squares; in which case does not appear at all in the final term.

 

Example

Q = f(a, b, c) = Σ(1, 2, 3, 6, 7)

-       Two prime implicant {1, 3} {2, 3, 6, 7}

-       Both are essential Q = Y + XZ