Procedure for Loading a Karnaugh Map and Determining the Essential Prime Implicants

1) Load min-terms into Karnaugh map by placing a 1 in the appropriate square.

2) Look for largest groups of min-terms, group must be a power of 2.

3) Look for largest groups of min-terms first, then progressively evaluate smaller collections of min-terms until all groups are found.

4) Once all possible prime implicants are determined, identify if they have min-terms that are unique. If so that Π is an Σ Π.

5) Select all Σ Π and a minimal set of the remaining Π so that all 1’s in the K-M are covered.

6) Move than one equally simplified result is possible when move than one set of remaining prime implicants contain the same number of min-terms on max-terms.

Example

F = f(x, y, z) = Σ(0, 2, 3, 4, 5, 7)

1) Π = {0, 2}; {2, 3}; {3, 7}; {2, 5}; {4, 5}; {0, 4}

2) Σ Π = Φ

3) Covering = {0, 2}; {3, 7}; {4, 5}

Example

K = f(w, x, y, z) = Σ(0, 1, 4, 5, 9, 11, 13, 15)

K = W’Y’ + WZ

Example

L = f(a, b, c, d) = Σ(0, 2, 5, 7, 8, 10, 13, 15)

L = bd + b’d’

Example

P = f(r, s, t, u) = Σ(1, 3, 4, 6, 9, 11, 12, 14)

P = s’u + su’

Example

D = f(w, x, y, z) = Σ(5, 7, 8, 9, 13)

D = w’xz + wx’y + wy’z