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Introduction to Boolean Algebra

📑 5 slides 👁 15 views 📅 2/14/2026
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What is Boolean Algebra?

Boolean algebra is a branch of mathematics dealing with true/false values (1/0).

What is Boolean Algebra?
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Basic Boolean Operations

  • AND: Output true only if all inputs are true (A ∧ B).
  • OR: Output true if at least one input is true (A ∨ B).
  • NOT: Inverts the input value (¬A).
  • XOR: Output true if inputs differ (A ⊕ B).
Basic Boolean Operations
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Boolean Algebra Laws

  • Identity Law: A AND 1 = A; A OR 0 = A
  • Commutative Law: A AND B = B AND A
  • Distributive Law: A AND (B OR C) = (A AND B) OR (A AND C)
  • De Morgan's Theorem: ¬(A AND B) = ¬A OR ¬B
Boolean Algebra Laws
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Applications in Computing

  • Forms basis for digital circuit design and logic gates.
  • Used in database query languages (SQL WHERE clauses).
  • Essential for programming conditional statements (if-else).
  • Underpins search algorithms and machine learning decision trees.
Applications in Computing
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Key Takeaways

  • Boolean algebra is fundamental to digital electronics and computer science.
  • Mastering basic operations and laws enables complex system design.
  • Applications range from simple circuits to advanced AI decision making.
  • Boolean principles remain relevant after 150+ years of technological advancement.
Key Takeaways
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