Boolean algebra

American  

[boo-lee-uhn] / ˈbu li ən /

noun

1. Logic. a deductive logical system, usually applied to classes, in which, under the operations of intersection and symmetric difference, classes are treated as algebraic quantities.

2. Mathematics. a ring with a multiplicative identity in which every element is an idempotent.

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Boolean algebra British  

/ ˈbuːlɪən /

noun

1. a system of symbolic logic devised by George Boole to codify logical operations. It is used in computers

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Boolean algebra Scientific  

/ bo̅o̅′lē-ən /

1. A form of symbolic logic, in which variables, which stand for propositions, have only the values “true” (or “1”) and “false” (or “0”). Relationships between these values are expressed by the Boolean operators AND, OR, and NOT. For example, “a + b” means “a OR b”, and its value is true as long as either a is true or b is true (or both). Boolean logic can be used to solve logical problems, and provides the mathematical tools fundamental to the design of digital computers. It is named after the mathematician George Boole.

2. Also called Boolean logic

3. See also logic gate

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Etymology

Origin of Boolean algebra

1885–90; named after George Boole; -an

Example Sentences

Venn’s success inspired other logicians to try to do the same with Boolean algebra.

From Salon • Jul. 29, 2024

Engineers now routinely design computer hardware and software, telephone networks and other complex systems with the aid of Boolean algebra.

From Scientific American • Jul. 30, 2017

Learn Boolean algebra, not just the basics to do logic, but the system by which logic can operate on the algebra itself.

From Forbes • Jul. 8, 2013

What parts of the brain are responsible for controlling various movements, functions and faculties, from aimless thumb-twiddling to Boolean algebra?

From Time Magazine Archive

The other was Alan Turing, who pointed out in the 1930s that, with Boolean algebra, only three logical functions are needed to process these "trues" and "falses";�or, in computer terms, Is and 0s.

From Time Magazine Archive