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In digital logic, a don't-care term (abbreviated DC, historically also known as redundancies, irrelevancies, optional entries, invalid combinations, vacuous combinations, forbidden combinations, unused states or logical remainders) for a function is an input-sequence (a series of bits) for which the function output does not matter.
This image actually shows two Karnaugh maps: for the function ƒ, using minterms (colored rectangles) and for its complement, using maxterms (gray rectangles). In the image, E () signifies a sum of minterms, denoted in the article as . The Karnaugh (/ˈkɑːnɔː/) map ( KM or K-map) is a method of simplifying Boolean algebra expressions.
The Quine–McCluskey algorithm ( QMC ), also known as the method of prime implicants, is a method used for minimization of Boolean functions that was developed by Willard V. Quine in 1952 [1] [2] and extended by Edward J. McCluskey in 1956. [3] As a general principle this approach had already been demonstrated by the logician Hugh McColl in ...
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 ...
In mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variables are the truth values true and false, usually denoted 1 and 0, whereas in elementary algebra the values of the variables are numbers. Second, Boolean algebra uses logical operators such ...
Canonical normal form. In Boolean algebra, any Boolean function can be expressed in the canonical disjunctive normal form ( CDNF ), [1] minterm canonical form, or Sum of Products ( SoP or SOP) as a disjunction (OR) of minterms. The De Morgan dual is the canonical conjunctive normal form ( CCNF ), maxterm canonical form, or Product of Sums ( PoS ...
In mathematics, the distributive property of binary operations is a generalization of the distributive law, which asserts that the equality. is always true in elementary algebra . For example, in elementary arithmetic, one has Therefore, one would say that multiplication distributes over addition . This basic property of numbers is part of the ...
The Boolean satisfiability problem (SAT) is, given a formula, to check whether it is satisfiable. This decision problem is of central importance in many areas of computer science, including theoretical computer science, complexity theory, [3] [4] algorithmics, cryptography [5] [6] and artificial intelligence. [7] [additional citation (s) needed]
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