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Quine–McCluskey Reducer

Systematic tabular Boolean minimisation for any number of variables

The Quine–McCluskey method is a tabular alternative to K-maps that scales to any number of variables and is the basis of commercial logic synthesis tools.

Three-stage process

1. Group minterms by count of 1-bits. 2. Merge pairs from adjacent groups differing by exactly one bit to produce prime implicants. 3. Cover table: select the minimum set of prime implicants covering every minterm.

When to use QM vs K-map

K-maps are faster for 4 variables or fewer. QM handles 5+ variables and is the only systematic method for programmatic minimisation.