📘 Unit 3 – Boolean Algebra (MCA)

 

1. Boolean Algebra Basics

• Boolean Algebra deals with variables that take two values only:

  • 0 (false/LOW)

  • 1 (true/HIGH)

• The main operations are:

  • AND (·) → Output is 1 if both inputs are 1.

  • OR (+) → Output is 1 if at least one input is 1.

  • NOT (') → Output is the complement of the input.

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2. Basic Boolean Laws

Here are some important laws of Boolean algebra:

• Identity Laws

  • A + 0 = A

  • A · 1 = A

• Null Laws

  • A + 1 = 1

  • A · 0 = 0

• Idempotent Laws

  • A + A = A

  • A · A = A

• Complement Laws

  • A + A' = 1

  • A · A' = 0

• Involution Law

  • (A')' = A

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3. DeMorgan’s Theorems

Two very important rules:

1. (A · B)' = A' + B'

2. (A + B)' = A' · B'

👉 These are very useful for simplification and circuit design.

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4. Duality Principle

Every Boolean expression remains valid if:

• + is replaced with ·

• 0 is replaced with 1
  (and vice versa).

Example:
(A + 0) = A
Dual → (A · 1) = A ✅

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5. Simplification Example

Simplify:
F = A · (B + B')

• B + B' = 1 (Complement Law)

• So F = A · 1 = A ✅