Boolean logic

1. Boolean logic

2. boolean logic

• Commutative – A ∧ B = B ∧ A; A ∨ B = B ∨ A
• Associative – (A ∧ B) ∧ C = A ∧ (B ∧ C)
• Distributive – A ∧ (B ∨ C) = (A ∧ B) ∨ (A ∧ C)
• Identity – A ∧ 1 = A; A ∨ 0 = A
• Null – A ∧ 0 = 0; A ∨ 1 = 1
• Double Negation – ¬(¬A) = A
• Complement – A ∧ ¬A = 0; A ∨ ¬A = 1
• De Morgan’s laws – ¬(A ∧ B) = ¬A ∨ ¬B; ¬(A ∨ B) = ¬A ∧ ¬B

3. Simplify using Boolean laws

•a) A ∧ A = ?
b) A ∨ (A ∧ B) = ?
c) (A ∨ B) ∧ (A ∨ ¬B) = ?
d) ¬(A ∨ B) = ?

4. Differentiation

• Level 1 (basic): Apply one simple law.
• Simplify: A ∧ 1
• Simplify: A ∨ 0
• Level 2 (intermediate): Apply two or more laws.
• Simplify: A ∨ (A ∧ B)
• Simplify: (A ∧ B) ∨ (A ∧ ¬B)
• Level 3 (advanced): Complex expressions requiring step-by-step
simplification.
• Simplify: (A ∨ B) ∧ (A ∨ ¬B)
• Simplify: (¬A ∨ B) ∧ (¬A ∨ ¬B)

5. Differentiation

• Level 1 (basic): Build a truth table.
• Construct a truth table for the expression: A ∨
(¬B)
• Level 2 (intermediate): Simplify expressions
using Boolean laws.
• Simplify: (A ∧ 1) ∨ (A ∧ 0)
• Simplify: (A ∨ B) ∧ (A ∨ ¬B)
• Level 3 (advanced): Combination of truth table
and simplification.

6.

• https://www.allaboutcircuits.com/textbook/digital/chpt-7/booleanalgebraic-identities/
• https://www.allaboutcircuits.com/textbook/digital/chpt-7/booleanalgebraic-identities/
• https://logic.ly/demo
• https://circuitverse.org/simulator