Boolean Algebra

Boolean algebra is a branch of mathematics that deals with variables that have two distinct values: typically represented as true ($1$) and false ($0$).

Developed by the English mathematician George Boole in the mid-19th century and described in his 1854 book, Boolean algebra provides a formal framework for analyzing and simplifying logical expressions and reasoning about logical operations. Boolean algebra is foundational in computer science, digital circuit design, and logic.

Boolean expressions are mathematical expressions that involve Boolean variables (= bits) and logical operations. They can represent logical propositions and can be evaluated to yield a Boolean value (true or false). A Boolean expression can be simple or complex, depending on the number of variables and operations involved.

Later, in the 20th century, Boolean Algebra became fundamental in electrical engineering and digital circuit design. The American mathematician and electrical engineer Claude Shannon showed that Boolean expressions can model switching circuits, and this connected logic with hardware.