/ |boolean| ˈældʒəbrə /
An algebra, fundamental to computer operations but developed in the mid-nineteenth century by English mathematician George Boole, for determining whether logical propositions are true or false rather than for determining the values of numerical expressions. In Boolean algebra, variables must have one of only two possible values, true or false, and relationships between these variables are expressed with logical operators, such as AND, OR, and NOT. Given these two-state variables and the relationships they can have to one another, Boolean algebra produces such propositions as C = A AND B, which means that C is true if and only if both A is true and B is true; thus, it can be used to process information and to solve problems. Furthermore, Boolean logic can be readily applied to the electronic circuitry used in digital computing. Like the binary numbers 1 and 0, true and false are easily represented by two contrasting physical states of a circuit, such as voltages, and computer circuits known as logic gates control the flow of electricity (bits of data) so as to represent AND, OR, NOT, and other Boolean operators. Within a computer, these logic gates are combined, with the output from one becoming the input to another so that the final result (still nothing more than sets of 1s and 0s) is meaningful data, such as the sum of two numbers. See the illustration. See also adder (definition 1), binary1, Boolean operator, gate (definition 1), logic circuit, truth table.
Set of algebraic rules, named for mathematician George Boole, in which TRUE and FALSE are equated to 0 and 1. Boolean algebra includes a series of operators (AND, OR, NOT, NAND (NOT AND), NOR, and XOR (exclusive OR)), which can be used to manipulate TRUE and FALSE values (see truth table). It is the basis of computer logic because the truth values can be directly associated with bits.