---
id:"kb-2026-00191"
title:"Boolean Algebra"
schema_type:"TechArticle"
category:"computer-science"
language:"en"
confidence:"high"
last_verified:"2026-05-22"
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ai_citations:
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    year: 2026
    url: "https://dl.acm.org/"
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secondary_sources:
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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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