Boolean Algebra

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## TL;DR

Boolean algebra (George Boole, 1854) is the mathematical foundation of digital logic and computer science. Variables are true/false. Operators: AND (conjunction), OR (disjunction), NOT (negation), XOR (exclusive OR). De Morgan's Laws: NOT(A AND B) = NOT A OR NOT B.

## Core Explanation

Truth tables enumerate all input combinations. Boolean algebra underlies: CPU logic gates, programming conditions, database WHERE clauses, search engines. NAND gate is functionally complete — any Boolean function can be built from NAND alone. Shannon (1938) first applied Boolean algebra to electrical circuit design in his MIT master's thesis.

## Further Reading

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## Related Articles

- [Linear Algebra](../linear-algebra.md)