The Quine–McCluskey method is algebraic simplification turned into a mechanical procedure, so it works for any number of variables and can be run by a computer.
Stage 1: find every prime implicant.
- Write each minterm (and don't-care) in binary. Group them by how many 1s they have; only neighboring groups can differ in exactly one bit.
- Compare every term in one group with every term in the next. If two differ in exactly one bit, combine them, putting a dash there, and tick both.
- Repeat with the new dashed terms. Two terms combine only if their dashes are in the same places.
- Any term never ticked is a prime implicant.
Stage 2: choose a minimal cover. Make a chart of which primes cover which minterms (not the don't-cares). Take the essential ones first, then add the cheapest primes for the minterms left.
It does exactly what a karnaugh map does by eye, but without relying on pattern-spotting. In practice, large problems use faster heuristic tools, built on the same ideas.