Karnaugh Maps - Rules of Simplification
The Karnaugh map uses the following rules for the simplification
of expressions by grouping together adjacent cells containing
- 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.
- No zeros allowed.
- No diagonals.
- Only power of 2 number of cells in each group.
- Groups should be as large as possible.
- Every one must be in at least one group.
- Overlapping allowed.
- Wrap around allowed.
- Fewest number of groups possible.
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Composed by David Belton - April 98