Algorithm for two-level simplification
Goal: deriving a minimum sum-of-products expression from a K-map
- Step 1: Choose an element of the ON-set
- Step 2: Find "maximal" groupings of 1s and Xs adjacent to that element
- Consider top/bottom row, left/right column, and corner adjacencies
- Form prime implicants (number of elements always a power of 2)
- Repeat Steps 1 and 2 to find all prime implicants
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- Step 3: Revisit the 1s in the K-map
- If covered by single prime implicant, it is essential, and participates in final cover
- 1s covered by essential prime implicant do not need to be revisited
- Step 4: If there remain 1s not covered by essential prime implicants
- Select the smallest number of prime implicants that cover the remaining 1s