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Karnaugh Map Tutorial

Minimize a Boolean function by circling groups on a Gray-code grid.

What a K-map is

A Karnaugh map is a truth table rearranged into a grid so that neighboring cells differ in exactly one input. Groups of adjacent 1s then correspond to simpler product terms.

Steps

1. Fill each cell with the function's output (1, 0, or X for don't care).
2. Circle rectangular groups of 1s. Group sizes must be a power of two: 1, 2, 4, 8, 16.
3. Make groups as large as possible. Groups may wrap around the edges, because the rows and columns are in Gray-code order (00, 01, 11, 10).
4. Cover every 1 with as few groups as possible. Don't-care cells may help a group grow, but need not be covered.
5. Each group becomes one AND term. Keep the variables that do not change inside the group. OR the terms together.

Example: majority of three

The function is 1 when at least two of A, B and C are 1. Its map has three groups of two cells, giving Y = A·B + B·C + A·C.

Terms to know

• A prime implicant is a group that cannot be made any larger.
• An essential prime implicant covers a 1 that no other prime implicant covers, so it must be in the answer.

The app's Analysis tab does this for you with the Quine-McCluskey method, draws the loops on the map, and can synthesize the resulting gates. See the manual chapter.