Karnaughmap

Karnaugh map (K-map) is a diagrammatic method used to simplify boolean algebra expressions. It was introduced by Maurice Karnaugh in 1953 and provides a visual approach to minimizing logic functions, typically in sum-of-products or product-of-sums form.

The map represents the truth table of a boolean function on a grid whose rows and columns are labeled by binary variables in Gray code order, so adjacent cells differ by only one variable. Each cell corresponds to a minterm, and the value inside the cell indicates the function output for that input combination. Don’t-care conditions can be marked to enable further simplification.

To minimize, groups of 1s are formed in powers of two (1, 2, 4, 8, …). Groups may wrap around the edges of the map. Each group yields a product term by identifying the variables that remain constant within the group; those constants form the literals of the term. The minimized expression is obtained by OR-ing the terms from all groups. In some cases, a prime implicant chart helps identify essential implicants.

Karnaugh maps are most practical for functions with up to six variables; for higher-dimensional functions, the maps become unwieldy and algorithms like Quine-McCluskey or computational tools are often used. K-maps remain a valuable educational tool and a useful heuristic for manual boolean minimization in digital logic design.