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First developed in the mid-1800s by mathematician George Boole, Boolean logic is a formal, mathematical approach to decision-making. Instead of the familiar algebra of symbols and numbers, Boole set down an algebra of decision states, such as yes and no, one and zero. The Boolean system remained in academia until the early 1900s, when electrical engineers noticed its usefulness for switching circuits, leading to telephone networks and digital computers.

## Boolean Algebra

Boolean algebra is a system for combining two-valued decision states and arriving at a two-valued outcome. In place of standard numbers, such as 15.2, Boolean algebra uses binary variables that can have two values, zero and one, which stand in for “false” and “true,” respectively. Instead of arithmetic, it has operations that combine binary variables to yield a binary result. For example, the “AND” operation gives a true result only if both of its arguments, or inputs, are also true. “1 AND 1 = 1,” but “1 AND 0 = 0” in Boolean algebra. The OR operation gives a true result if either argument is true. “1 OR 0 = 1,” and “0 OR 0 = 0” both illustrate the OR operation.

## Digital Circuits

Boolean algebra benefited electrical designers in the 1930s who worked on telephone switching circuits. Using Boolean algebra, they set a closed switch equal to one, or “true,” and an open switch to be zero, or “false.” The same advantage applies to the digital circuits comprising computers. Here, a high voltage state equals a “true” and a low voltage state equals a “false.” Using high and low voltage states and Boolean logic, engineers developed digital electronic circuits that could solve simple yes-no decision-making problems.