booleaans

Booleans are a data type that encodes truth values, typically true and false. They are central to modern computing and logic. The concept derives from Boolean algebra, developed by George Boole in the 19th century, which uses algebraic operations and laws to model logical relations. In digital systems, booleans underpin decision-making and control flows.

In software, booleans represent the results of logical tests and control flow decisions. They participate in conditional expressions, loops, and branching. Basic boolean operations include AND, OR, and NOT, with XOR as exclusive OR. Truth tables define how these operations combine inputs to yield outputs. In hardware, these operations map to logic gates that drive circuits.

Boolean algebra satisfies properties such as commutativity, associativity, and distributivity, and obeys De Morgan's laws, which relate complements of conjunctions and disjunctions. These rules enable simplification of complex logical expressions and optimization of circuits.

Most programming languages implement booleans as a distinct type with values true and false. Some languages also assign a truthiness value to other data, where 0 or empty values count as false and nonzero values as true. In SQL and databases, three-valued logic adds UNKNOWN to true and false, often represented by NULL.

Beyond software, boolean logic forms the basis of digital electronics and information theory. Boolean expressions are translated into circuits of AND, OR, and NOT gates, enabling computation, data storage, and communication systems.