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The Karnaugh map (KM or K-map) is a method of simplifying Boolean algebra expressions. Maurice Karnaugh introduced it in 1953 [1] [2] as a refinement of Edward W. Veitch 's 1952 Veitch chart , [3] [4] which itself was a rediscovery of Allan Marquand 's 1881 logical diagram [5] [6] aka Marquand diagram [4] but now with a focus set on its utility ...
"For more than three variables, the basic illustrative form of the Venn diagram is inadequate. Extensions are possible, however, the most convenient of which is the Karnaugh map, to be discussed in Chapter 6." (p 64) In Chapter 6, section 6.4 "Karnaugh map representation of Boolean functions" they begin with:
In Boolean algebra, the consensus theorem or rule of consensus [1] is the identity: The consensus or resolvent of the terms and is . It is the conjunction of all the unique literals of the terms, excluding the literal that appears unnegated in one term and negated in the other. If includes a term that is negated in (or vice versa), the ...
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The figure shows a function of three variables, P(A, B, C) represented as a Karnaugh map, which the reader may consider as an example of how to convert such maps into Zhegalkin polynomials; the general procedure is given in the following steps: We consider all the cells of the Karnaugh map in ascending order of the number of units in their codes.
Canonical normal form is a mathematical concept that describes the simplest way of representing a function or a relation. It is useful for simplifying expressions, solving equations, and comparing different forms of the same function. Learn more about the definition, properties, and examples of canonical normal form on Wikipedia.
Logic optimization is a process of finding an equivalent representation of the specified logic circuit under one or more specified constraints. This process is a part of a logic synthesis applied in digital electronics and integrated circuit design . Generally, the circuit is constrained to a minimum chip area meeting a predefined response delay.
Disjunctive normal form. In boolean logic, a disjunctive normal form ( DNF) is a canonical normal form of a logical formula consisting of a disjunction of conjunctions; it can also be described as an OR of ANDs, a sum of products, or — in philosophical logic — a cluster concept. [1] As a normal form, it is useful in automated theorem proving .