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Boolean algebra, a logical calculus of truth values or set membership; Boolean algebra (structure), a set with operations resembling logical ones; Boolean circuit, a mathematical model for digital logical circuits. Boolean data type is a data type, having two values (usually denoted true and false)
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.
The term "Boolean algebra" honors George Boole (1815–1864), a self-educated English mathematician. He introduced the algebraic system initially in a small pamphlet, The Mathematical Analysis of Logic, published in 1847 in response to an ongoing public controversy between Augustus De Morgan and William Hamilton, and later as a more substantial book, The Laws of Thought, published in 1854.
Boolean algebra is a mathematically rich branch of abstract algebra. Stanford Encyclopaedia of Philosophy defines Boolean algebra as 'the algebra of two-valued logic with only sentential connectives, or equivalently of algebras of sets under union and complementation.' [1] Just as group theory deals with groups, and linear algebra with vector spaces, Boolean algebras are models of the ...
In fact, however, Boole's algebra differs from modern Boolean algebra: in Boole's algebra A+B cannot be interpreted by set union, due to the permissibility of uninterpretable terms in Boole's calculus. Therefore, algebras on Boole's account cannot be interpreted by sets under the operations of union, intersection and complement, as is the case ...
A timeline of mathematical logic ; see also history of logic. 19th century 1847 – George Boole proposes symbolic logic in The Mathematical Analysis of Logic, defining what is now called Boolean algebra. 1854 – George Boole perfects his ideas, with the publication of An Investigation of the Laws of Thought. 1874 – Georg Cantor proves that the set of all real numbers is uncountably ...
A revolutionary work for switching circuit theory, Shannon diagramed switching circuits that could implement the essential operators of Boolean algebra. Then he proved that his switching circuits could be used to simplify the arrangement of the electromechanical relays that were used during that time in telephone call routing switches. Next, he ...
B. Balanced Boolean function; Bent function; Binary decision diagram; Bitwise operation; George Boole; Boole's expansion theorem; Boolean algebras canonically defined