Quine-McCluskey Boolean Minimizer
Minimize a sum-of-products boolean function given its minterms (and optional don't-care terms) using the Quine-McCluskey algorithm — the tabular method that is guaranteed to find a minimal two-level SOP form, equivalent to a Karnaugh map but algorithmic and exact. It generates all prime implicants, selects the essential ones, and uses Petrick's method to cover any remaining minterms with the fewest implicants. The prime-implicant chart and each step are shown. Everything runs locally in your browser.
Minimized SOP
Prime implicants
Prime implicant chart
Quine-McCluskey minimizes a boolean function exactly. Step 1 — list every minterm (and don't-care) as an n-bit binary string and repeatedly combine pairs that differ in exactly one bit, replacing that bit with –; terms that combine no further are prime implicants. Step 2 — build the prime implicant chart: each row is a prime implicant, each column a minterm (don't-cares are not covered). A essential prime implicant is the only one covering some minterm — it must be in the answer. Step 3 — if minterms remain, Petrick's method ANDs together one (Pᵢ ∨ Pⱼ ∨ …) clause per uncovered minterm, expands the product-of-sums into a sum-of-products of prime-implicant sets, and picks the set with the fewest implicants (and fewest literals), giving a minimal cover. Variables are named A, B, C… with A as the most-significant bit, matching the Truth Table Generator. Pairs with that tool. Everything runs locally — nothing leaves your browser.