Definition, Meaning & Synonyms | English word BOOLEAN

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Definitions of BOOLEAN

1. Of or pertaining to the work of George Boole.
2. (logic, computing) Pertaining to data items that can have “true” and “false” (or, equivalently, 1 and 0 respectively) as their only possible values and to operations on such values.
3. (logic, computing) A variable that can hold a single true/false (1/0) value.
4. Alternative letter-case form of Boolean.

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Examples of Using BOOLEAN in a Sentence

• A Boolean algebra can be seen as a generalization of a power set algebra or a field of sets, or its elements can be viewed as generalized truth values.
• In logic and computer science, the Boolean satisfiability problem (sometimes called propositional satisfiability problem and abbreviated SATISFIABILITY, SAT or B-SAT) is the problem of determining if there exists an interpretation that satisfies a given Boolean formula.
• The success and failure of a given block of code is used to direct further processing, whereas conventional languages would typically use boolean logic written by the programmer to achieve the same ends.
• A logic gate is a device that performs a Boolean function, a logical operation performed on one or more binary inputs that produces a single binary output.
• In Boolean logic, the majority function (also called the median operator) is the Boolean function that evaluates to false when half or more arguments are false and true otherwise, i.
• In Boolean functions and propositional calculus, the Sheffer stroke denotes a logical operation that is equivalent to the negation of the conjunction operation, expressed in ordinary language as "not both".
• Boolean logic, essential to computer programming, is credited with helping to lay the foundations for the Information Age.
• In telecommunication, a convolutional code is a type of error-correcting code that generates parity symbols via the sliding application of a boolean polynomial function to a data stream.
• More specific complete lattices are complete Boolean algebras and complete Heyting algebras (locales).
• Boolean logic is a system of syllogistic logic invented by 19th-century British mathematician George Boole, which attempts to incorporate the "empty set", that is, a class of non-existent entities, such as round squares, without resorting to uncertain truth values.
• Every Boolean ring gives rise to a Boolean algebra, with ring multiplication corresponding to conjunction or meet , and ring addition to exclusive disjunction or symmetric difference (not disjunction , which would constitute a semiring).
• One example of a co-NP-complete problem is tautology, the problem of determining whether a given Boolean formula is a tautology; that is, whether every possible assignment of true/false values to variables yields a true statement.
• Problems known to be PSPACE-complete include determining properties of regular expressions and context-sensitive grammars, determining the truth of quantified Boolean formulas, step-by-step changes between solutions of combinatorial optimization problems, and many puzzles and games.
• In propositional logic and Boolean algebra, De Morgan's laws, also known as De Morgan's theorem, are a pair of transformation rules that are both valid rules of inference.
• In Boolean logic, a formula is in conjunctive normal form (CNF) or clausal normal form if it is a conjunction of one or more clauses, where a clause is a disjunction of literals; otherwise put, it is a product of sums or an AND of ORs.
• Examples of structures with two operations that are each distributive over the other are Boolean algebras such as the algebra of sets or the switching algebra.
• It pioneered many features that would become common in languages from the 1960s into the 1980s, including use of line numbers as both editing instructions and targets for branches, statements predicated by boolean decisions, and a built-in source-code editor that can perform instructions in direct or immediate mode, what they termed a conversational user interface.
• The pixels of each are combined using a program-selectable raster operation, a bit-wise boolean formula.
• Algebraically, classical negation corresponds to complementation in a Boolean algebra, and intuitionistic negation to pseudocomplementation in a Heyting algebra.
• In some programming languages, any expression can be evaluated in a context that expects a Boolean data type.

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