Skip to main content

Karnaugh map

Karnaugh map (Veitch diagram) A graphical means for representing Boolean expressions so that the manner in which they can be simplified or minimized is made apparent. It may be regarded as a pictorial representation of a truth table or as an extension of the Venn diagram. The method was proposed by E. W. Veitch and modified slightly by M. Karnaugh. The Karnaugh maps for expressions involving one, two, three, and four variables are shown in the diagram. When n = 2, for instance, the 00 square represents the term a′b′ (where ′ denotes negation), the 11 square represents ab, and so on.

Terms that differ in precisely one variable can be combined. Such terms will appear as adjacent squares on a Karnaugh map and so can readily be identified. For example, the terms abc and abc′ can be combined since abcabc′ = ab

These two terms should each occupy one square on the n = 3 map and appear side by side, i.e. share a common edge. However, so too should the a′b′c and the ab′c squares. This complication can be overcome by stipulating that the two edges marked with dashes should be identified or joined together, i.e. the Karnaugh map for n = 3 should be drawn on one side of a ring of paper. When n = 4 the situation is even more complex: the two edges marked with dashes are identified, as are the dotted edges. The map can then be viewed as drawn on the outside of a torus.

Karnaugh maps are useful for expressions of perhaps up to six variables. When n > 6, the maps become unwieldy and too complex. Alternative methods of simplification, such as the Quine–McCluskey algorithm, are then preferable.

Cite this article
Pick a style below, and copy the text for your bibliography.

  • MLA
  • Chicago
  • APA

"Karnaugh map." A Dictionary of Computing. . 24 Apr. 2019 <>.

"Karnaugh map." A Dictionary of Computing. . (April 24, 2019).

"Karnaugh map." A Dictionary of Computing. . Retrieved April 24, 2019 from

Learn more about citation styles

Citation styles gives you the ability to cite reference entries and articles according to common styles from the Modern Language Association (MLA), The Chicago Manual of Style, and the American Psychological Association (APA).

Within the “Cite this article” tool, pick a style to see how all available information looks when formatted according to that style. Then, copy and paste the text into your bibliography or works cited list.

Because each style has its own formatting nuances that evolve over time and not all information is available for every reference entry or article, cannot guarantee each citation it generates. Therefore, it’s best to use citations as a starting point before checking the style against your school or publication’s requirements and the most-recent information available at these sites:

Modern Language Association

The Chicago Manual of Style

American Psychological Association

  • Most online reference entries and articles do not have page numbers. Therefore, that information is unavailable for most content. However, the date of retrieval is often important. Refer to each style’s convention regarding the best way to format page numbers and retrieval dates.
  • In addition to the MLA, Chicago, and APA styles, your school, university, publication, or institution may have its own requirements for citations. Therefore, be sure to refer to those guidelines when editing your bibliography or works cited list.