Karnaugh Maps - Rules of Simplification

The Karnaugh map uses the following rules for the simplification of expressions by grouping together adjacent cells containing ones

• Groups may not include any cell containing a zero

• Groups may be horizontal or vertical, but not diagonal.

• Groups must contain 1, 2, 4, 8, or in general 2n cells.
That is if n = 1, a group will contain two 1's since 21 = 2.
If n = 2, a group will contain four 1's since 22 = 4.

• Each group should be as large as possible.

• Each cell containing a one must be in at least one group.

• Groups may overlap.

• Groups may wrap around the table. The leftmost cell in a row may be grouped with the rightmost cell and the top cell in a column may be grouped with the bottom cell.

• There should be as few groups as possible, as long as this does not contradict any of the previous rules.

Summmary:

1. No zeros allowed.
2. No diagonals.
3. Only power of 2 number of cells in each group.
4. Groups should be as large as possible.
5. Every one must be in at least one group.
6. Overlapping allowed.
7. Wrap around allowed.
8. Fewest number of groups possible.

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