Boolean Algebra Operations - Complete Guide

Boolean Algebra Operations - Complete Guide

Class: 11-12 | Subject: Computer Science/Math | Exam: HSC/University

What is Boolean Algebra?

Boolean Algebra is a mathematical system for logical operations using binary values: 1 (true) and 0 (false).

Basic Operations

Operation	Symbol	Description	Truth Table
AND	· or ∧	Output 1 only if all inputs are 1	A·B = 1 when A=1 AND B=1
OR	+ or ∨	Output 1 if any input is 1	A+B = 1 when A=1 OR B=1
NOT	¬ or ' or ~	Inverts the input	¬A = 1 when A=0

Boolean Laws

Identity Law:    A + 0 = A       A · 1 = A
Complement Law:  A + ¬A = 1      A · ¬A = 0
Commutative Law: A + B = B + A   A · B = B · A
Distributive:    A·(B+C) = A·B + A·C

Example Problem (HSC Level)

Simplify: (A + B)·(¬A + C)

1. Apply Distributive Law: A·¬A + A·C + B·¬A + B·C
2. Simplify using Complement: 0 + A·C + B·¬A + B·C
3. Final form: A·C + B·¬A + B·C

Practice Exercise

Simplify using Boolean laws:

1. A + A·B
2. (A + B)·(A + C)

1. A
2. A + B·C

Applications

• Digital circuit design
• Computer programming (if-else logic)
• Database search queries