Karnaugh Map
Karnaugh map
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Jump to: navigation, search | This article includes a list of references, but its sources remain unclear because it has insufficient inline citations. Please help to improve this article by introducing more precise citations where appropriate. (June 2010) |
For former radio station KMAP (1962-1968) in Dallas-Fort Worth, see KRLD-FM.
An example Karnaugh map
The Karnaugh map (K-map for short), Maurice Karnaugh's 1953 refinement of Edward Veitch's 1952 Veitch diagram, is a method to simplify Boolean algebra expressions. The Karnaugh map reduces the need for extensive calculations by taking advantage of humans' pattern-recognition capability, permitting the rapid identification and elimination of potential race conditions.
In a Karnaugh map the boolean variables are transferred (generally from a truth table) and ordered according to the principles of Gray code in which only one variable changes in between adjacent squares. Once the table is generated and the output possibilities are transcribed, the data is arranged into the largest possible groups containing 2n cells (n=0,1,2,3...)[1] and the minterm is generated through the axiom laws of boolean algebra. Contents[hide] * 1 Example * 1.1 Truth table * 1.2 Karnaugh map * 1.3 Solution * 1.4 Inverse * 1.5 Don't cares * 2 Race hazards * 2.1 Elimination * 2.2 2-variable map examples * 3 See also * 4 References * 5 Further reading * 6 External links |
[edit] Example
Karnaugh maps are used to facilitate the simplification of Boolean algebra functions. The following is an unsimplified Boolean Algebra function with Boolean variables A, B, C, D, and their inverses. They can be represented in two different notations: * f(A,B,C,D,E) = ∑(6,8,9,10,11,12,13,14) Note: The values inside ∑ are the minterms to map (i.e. rows which have output 1 in the truth table).
*
[edit] Truth table
Using the
From Wikipedia, the free encyclopedia
Jump to: navigation, search | This article includes a list of references, but its sources remain unclear because it has insufficient inline citations. Please help to improve this article by introducing more precise citations where appropriate. (June 2010) |
For former radio station KMAP (1962-1968) in Dallas-Fort Worth, see KRLD-FM.
An example Karnaugh map
The Karnaugh map (K-map for short), Maurice Karnaugh's 1953 refinement of Edward Veitch's 1952 Veitch diagram, is a method to simplify Boolean algebra expressions. The Karnaugh map reduces the need for extensive calculations by taking advantage of humans' pattern-recognition capability, permitting the rapid identification and elimination of potential race conditions.
In a Karnaugh map the boolean variables are transferred (generally from a truth table) and ordered according to the principles of Gray code in which only one variable changes in between adjacent squares. Once the table is generated and the output possibilities are transcribed, the data is arranged into the largest possible groups containing 2n cells (n=0,1,2,3...)[1] and the minterm is generated through the axiom laws of boolean algebra. Contents[hide] * 1 Example * 1.1 Truth table * 1.2 Karnaugh map * 1.3 Solution * 1.4 Inverse * 1.5 Don't cares * 2 Race hazards * 2.1 Elimination * 2.2 2-variable map examples * 3 See also * 4 References * 5 Further reading * 6 External links |
[edit] Example
Karnaugh maps are used to facilitate the simplification of Boolean algebra functions. The following is an unsimplified Boolean Algebra function with Boolean variables A, B, C, D, and their inverses. They can be represented in two different notations: * f(A,B,C,D,E) = ∑(6,8,9,10,11,12,13,14) Note: The values inside ∑ are the minterms to map (i.e. rows which have output 1 in the truth table).
*
[edit] Truth table
Using the