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Karnaugh Maps (K-Maps)

A graphical method used for simplifying Boolean functions. It visually groups adjacent '1's in a truth table to derive the minimal Sum-of-Products (SOP) expression.
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The statement of the theorem

Given a Boolean function f(x1,…,xn)f(x_1, \dots, x_n) defined by its minterms ∑mi\sum m_i, the K-Map method identifies the minimal set of prime implicants by grouping adjacent '1's in the truth table representation. Adjacency is defined by Hamming distance 1 (or 2k2^k grouping). The minimal SOP expression is formed by the union of the essential prime implicants, min(f)=∑Pi\text{min}(f) = \sum P_i, where PiP_i are the prime implicants covering all minterms of ff with the minimum possible cardinality.