A fast-lookup reference for the grouping rules — for the full explanation of why each rule works, see What Is a Karnaugh Map?. This page is the checklist version.
The core rules
- Group sizes must be a power of 2 — 1, 2, 4, 8, 16 cells. Never 3, 5, 6, or 7.
- Groups must be rectangular, including wraparound rectangles across map edges.
- The map wraps at every edge — leftmost/rightmost columns are adjacent, top/bottom rows are adjacent. See K-Map Wraparound for every edge case illustrated.
- Every required 1 (and any don't-care you choose to use) must be covered by at least one group.
- Groups may overlap — the same cell can belong to more than one group at once.
- Find all maximal groups, then choose a cover across the whole map — a locally largest group can leave more terms than another combination. See the cover-selection guide and Petrick's method.
Group size → literals dropped
| Group size | Variables dropped | Effect |
|---|---|---|
| 1 cell | 0 | Full term, every variable present |
| 2 cells | 1 | One literal drops out |
| 4 cells | 2 | Two literals drop out |
| 8 cells | 3 | Three literals drop out |
| 16 cells | 4 | Entire function is constant (all 1s or the whole map) |
Each doubling drops one more variable from that individual term. It does not by itself minimize the complete expression: include all essential prime implicants, then choose a minimum cover for the remaining cells. This solver minimizes term count first and literal count among ties; follow the objective stated by your assignment.
Priority order when several groupings are possible
- Identify every prime implicant (every maximal valid group — one that can't be made any larger).
- Mark essential prime implicants first — any group that's the only one covering some required cell. See Essential vs. Non-Essential Prime Implicants.
- For anything still uncovered after essential groups are selected, resolve the remaining choice with Petrick's method rather than guessing.
Common failure modes
The five specific mistakes that cause most lost points are covered in full, with worked examples, in Common Karnaugh Map Mistakes — missed wraparound, undersized groups, invalid shapes, missed cyclic charts, and SOP/POS grouping mix-ups.
Apply all of this directly on the K-map solver, which shows the actual grouping and prime implicant classification for whatever you enter.