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The Karnaugh map reduces the need for extensive calculations by taking advantage of humans’ pattern-recognition capability. These terms can be used to write a minimal Boolean expression representing the required logic. Karnaugh maps are used to simplify real-world logic requirements so that they can be implemented using a minimum number of physical logic gates. OR gates feeding an AND gate. Karnaugh maps can also be used to simplify logic expressions in software design.

Once minimised, canonical sum-of-products and product-of-sums expressions can be implemented directly using AND and OR logic operators. K-map drawn on a torus, and in a plane. The dot-marked cells are adjacent. In three dimensions, one can bend a rectangle into a torus.

In the example above, the four input variables can be combined in 16 different ways, so the truth table has 16 rows, and the Karnaugh map has 16 positions. Gray code ensures that only one variable changes between each pair of adjacent cells. Each cell of the completed Karnaugh map contains a binary digit representing the function’s output for that combination of inputs. Adjacent 1s in the Karnaugh map represent opportunities to simplify the expression. Minterm rectangles should be as large as possible without containing any 0s.

Groups may overlap in order to make each one larger. The optimal groupings in the example below are marked by the green, red and blue lines, and the red and green groups overlap. 1 rectangle, and the overlap area is indicated in brown. The cells are often denoted by a shorthand which describes the logical value of the inputs that the cell covers.