Question

Prime implicants and non prime implicants example in k maps

Answer 1

Implicant
A normal product term that implies Y.
Example: For the function Y = AB + ABC + BC, the implicants are AB, ABC, and BC because if any one of those terms are true, then Y is true.
Prime Implicant
An implicant of Y such that if any variable is removed from the implicant, the resulting term does not imply Y.
Example: Y = AB + ABC + BC
Prime Implicants: AB, BC
Not a prime implicant: ABC
ABC is not a prime implicant because the literal A can be removed to give BC and BC still implies Y. Conversely AB is not a prime implicant because you can't remove either A or B and have the remaining term still imply Y.
In truth tables the prime implicants are represented by the largest rectangular groups of ones that can be circled. If a smaller subgroup is circled, the smaller group is an implicant, but not a prime implicant.



Karnaugh Map Examples

In the following examples the distinguished 1-cells are marked in the upper left corner of the cell with an asterisk (*). The essential prime implicants are circled in blue, the prime implicants are circled in black, and the non-essential prime implicants included in the minimal sum are shown in red.

Example 1

Prime Implicants: 5
Distinguished 1-Cells: 2
Essential Prime Implicants: 2
Minimal Sums: 1


Y = A'CD' + AC'D + BCD