K-Map Grouping Rules: The Quick-Reference Cheat Sheet

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.
  • Always take the largest valid group available before settling for a smaller one — see Overlapping Groups in K-Maps for exactly when a smaller group is still the right call.

Group size → literals dropped

Group sizeVariables droppedEffect
1 cell0Full term, every variable present
2 cells1One literal drops out
4 cells2Two literals drop out
8 cells3Three literals drop out
16 cells4Entire function is constant (all 1s or the whole map)

Every doubling in group size drops exactly one more variable from the resulting term — which is why always reaching for the largest valid group directly minimizes literal count.

Priority order when several groupings are possible

  1. Identify every prime implicant (every maximal valid group — one that can't be made any larger).
  2. Mark essential prime implicants first — any group that's the only one covering some required cell. See Essential vs. Non-Essential Prime Implicants.
  3. 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.

Try it on the solver

Work through the examples above directly — enter the same minterms or expression into the live tool.

Open the K-Map Solver