Karnaugh Map Solver

Karnaugh map solver with groupings and step-by-step minimisation

This Karnaugh map solver simplifies a Boolean function of 2, 3, 4 or 5 variables to its minimal sum-of-products or product-of-sums form. Enter the minterms (the rows of the truth table where the output is 1) and any don’t-care conditions, or simply click cells on the map to toggle them between 0, 1 and X. The map is drawn in Gray-code order, each chosen group is outlined in its own colour — including groups that wrap around the edges — and the resulting expression appears above it.

Because K-maps are solved by eye, the tool uses the equivalent algorithm, Quine–McCluskey with Petrick’s method, to guarantee a minimal cover and to show the working: the grouping of minterms by their number of 1s, each combining round, the prime implicants, the essential ones, and the choice made among the remaining candidates.

How to use the Karnaugh Map Solver

1. Choose the number of Variables (2–5). Variables are named A, B, C, D, E with A as the most significant bit of the minterm number.
2. Type the Minterms as a comma-separated list, such as 0, 1, 2, 5, 6, 7, and any Don’t-cares. Alternatively paste a truth-table output column such as 11100111.
3. Or click cells on the map: each click cycles 0 → 1 → X → 0, and the lists update to match.
4. Read the minimal expression above the map. Switch between Minimal SOP and Minimal POS, and pick the notation (A'B, ĀB or ¬A∧B).
5. Follow the numbered Solution steps to see the prime implicants, the essential ones and the Petrick selection if the chart is cyclic.
6. Copy the expression as text or LaTeX, or download the map as SVG for a report.

Karnaugh Map Solver features

How a Karnaugh map works

A Karnaugh map is a truth table folded into a grid whose rows and columns are numbered in Gray code (00, 01, 11, 10), so that any two cells that touch — including cells at opposite edges — differ in exactly one variable. Wherever a block of 1-cells with 2, 4, 8 or 16 members forms a rectangle, the variables that change inside that block cancel out, leaving a product term with fewer literals. The minimal SOP is the smallest set of such blocks (prime implicants) that covers every 1-cell; don’t-cares may be included in a block whenever that makes it larger.

The product-of-sums form uses the same idea on the 0-cells: each block of zeros becomes a sum term in which every literal is complemented, so a block where A = 1 and B = 0 gives the factor (A' + B).

Worked example: F = Σm(0, 1, 2, 5, 6, 7)

With three variables the 1-cells are 000, 001, 010, 101, 110 and 111. Every pair of adjacent 1s forms a two-cell group, giving six prime implicants — A'B', A'C', B'C, AC, AB and BC' — and none of them is essential, because every minterm sits in two groups. This is a cyclic chart, where a quick glance can lead to four groups when three suffice. Petrick’s method shows that two different three-term covers exist: A'B' + BC' + AC and A'C' + B'C + AB; both use six literals, and the solver reports one of them. The POS form comes from the two 0-cells (011 and 100): F = (A + B' + C')(A' + B + C).

Tips and common mistakes

• Groups must be rectangles whose side lengths are powers of two: 1, 2, 4 or 8 cells. An L-shape or a 3-cell strip is not a valid group.
• Always look for wrap-around groups — the four corner cells of a 4-variable map form a valid group (B'D' in the usual labelling).
• Use the largest possible groups, even if cells are covered twice; redundant small groups add literals without changing the function.
• If a cell is a don’t-care, you are free to treat it as 0 for SOP and 1 for POS; the two minimal forms may therefore assign it differently.
• To build the minterm list from an expression, run it through the truth table generator, which prints Σm(…) directly; the bitwise calculator helps when the function is given as a hex bit pattern.