What to do
A Karnaugh map helps you simplify a Boolean expression by grouping cells that contain 1s. The goal is to rewrite the expression in a shorter form while keeping the same truth values.
Step-by-step method
- Read the map carefully. Identify which cells are marked 1. If the map uses don’t-care entries, they may be used to help make larger groups when allowed.
- Group adjacent 1s. Make rectangular groups of size 1, 2, 4, 8, etc. Use the largest possible groups first.
- Use wraparound adjacency. Cells on opposite edges of the map may count as neighbors if the map layout connects them.
- Cover every 1. Each 1 must belong to at least one group. Overlapping groups are allowed if they help simplify the result.
- Write one term per group. For each group, keep only the variables that stay constant across all cells in that group. Variables that change are removed.
- Combine the terms. Add the group terms using OR to form the simplified expression.
Check your answer
Verify that every original 1 is covered and that no extra minterms are introduced. If possible, compare the simplified expression to the map by evaluating a few cases or by checking that the groups match the unchanged variables correctly.
Tips
- Prefer the fewest groups and the largest groups.
- A single isolated 1 becomes a term with all its variables.
- Do not forget edge connections and corner possibilities when the map layout allows them.