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The Karnaugh map, also known as the K-map, is a method to simplify boolean algebra expressions. Maurice Karnaugh introduced it in 1953 as a refinement of Edward Veitch's 1952 Veitch diagram. The Karnaugh map reduces the need for extensive calculations by taking advantage of humans' pattern-recognition capability. It also permits the rapid identification and elimination of potential race conditions. The required boolean results are transferred from a truth table onto a two-dimensional grid where the cells are ordered in Gray code, and each cell position represents one combination of input conditions, while each cell value represents the corresponding output value. Optimal groups of 1s or 0s are identified, which represent the terms of a canonical form of the logic in the original truth table.〔(【引用サイトリンク】title=Karnaugh Maps – Rules of Simplification )〕 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. A sum-of-products expression can always be implemented using AND gates feeding into an OR gate, and a product-of-sums expression leads to OR gates feeding an AND gate.〔(【引用サイトリンク】url=http://www.utdallas.edu/~dodge/EE2310/lec5.pdf )〕 Karnaugh maps can also be used to simplify logic expressions in software design. Boolean conditions, as used for example in conditional statements, can get very complicated, which makes the code difficult to read and to maintain. Once minimised, canonical sum-of-products and product-of-sums expressions can be implemented directly using AND and OR logic operators. ==Example== Karnaugh maps are used to facilitate the simplification of Boolean algebra functions. Take the Boolean function described by the following truth table. Following are two different notations describing the same function in unsimplified Boolean algebra, using the Boolean variables , , , , and their inverses. * where are the maxterms to map (i.e., rows that have output 0 in the truth table). 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Karnaugh map」の詳細全文を読む スポンサード リンク
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