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Boolean Algebra

In mathematics and mathematical logic, Boolean algebra is the subarea of algebra. In elementary algebra the values of the variables are numbers, and the main operations are addition and multiplication. In comparison the values of the variables in Boolean algebra are the binary truth values true and false, which are usually identified with the bits and denoted by 0 and 1 (respectively). The main operations of Boolean algebra are instead the logical connectives conjunction (AND), disjunction (OR), and negation (NOT). Boolean algebra defines the rules by which the problem of determining whether the variables of a given Boolean formula evaluate to true or false can be solved. Most logical operations connect two logical input values and produces a distinct logical output truth value. The valuation is based on logical reasoning.

NOT 1 = 0 (meaning NOT true = false),
NOT 0 = 1 (meaning NOT false = true),
1 AND 0 = 0 (meaning true AND false = false),
1 OR 0 = 1 (meaning true OR false = true),
1 AND 1 = 1 (meaning true AND true = true),
1 OR 1 = 1 (meaning true OR true = true)

Boolean algebra has been fundamental in the development of computer science and is yet the basis of the abstract description of digital circuits. A digital circuit is often constructed from circuits called logic gates that represent a function of Boolean algebra.

Konrad Zuse used Boolean algebra in the design of his computers for the construction of binary switching elements and logic gates.

cf. Wikipedia