In this note, we are going to learn about Boolean Algebra Laws and Rules in Digital Electronics. Welcome to Poly Notes Hub, a leading destination for diploma or polytechnic engineering notes.

Author Name: Arun Paul.

Introduction

Boolean algebra is an area of mathematics that analyzes and simplifies digital (logic) circuits. It handles binary numbers 0 and 1 and defines rules for processing logical expressions.

These laws contribute to simplifying complex logic circuits. If you want to download this note PDF, then click on Printer Icon Below.

Basic Boolean Operators

Symbol	Meaning	Type
·	AND	Boolean AND Operator
+	OR	Boolean OR Operator
‘	NOT	Boolean NOT Operator

Different Types of Boolean Algebra Laws and Rules in Digital Electronics

There are 11 types of Boolean Algebra Laws, those are –

• Commutative Laws
• Associative Laws
• Distributive Laws
• Identity Laws
• Null / Dominance Laws
• Idempotent Laws
• Complement Laws
• Involution Law
• Absorption Laws
• Consensus Theorem
• De Morgan’s Theorem

Formulas of Different Laws of Boolean Algebra

Here we have listed all the expressions or formulas of Boolean Algebra of Digital Electronics –

Category	Law / Formula	Expression
Commutative Laws	OR Commutative	A + B = B + A
	AND Commutative	A · B = B · A
Associative Laws	OR Associative	(A + B) + C = A + (B + C)
	AND Associative	(A · B) · C = A · (B · C)
Distributive Laws	AND over OR	A(B + C) = AB + AC
	OR over AND	A + (BC) = (A + B)(A + C)
Identity Laws	OR Identity	A + 0 = A
	AND Identity	A · 1 = A
Null / Dominance Laws	OR Null	A + 1 = 1
	AND Null	A · 0 = 0
Idempotent Laws	OR Idempotent	A + A = A
	AND Idempotent	A · A = A
Complement Laws	OR Complement	A + A’ = 1
	AND Complement	A · A’ = 0
Involution Law	Double Complement	(A’)’ = A
Absorption Laws	Absorption 1	A + AB = A
	Absorption 2	A(A + B) = A
Consensus Theorem	Consensus 1	AB + A’C + BC = AB + A’C
	Consensus 2	(A + B)(A’ + C)(B + C) = (A + B)(A’ + C)
De Morgan’s Theorem	First Theorem	(A · B)’ = A’ + B’
	Second Theorem	(A + B)’ = A’ · B’
Useful Simplification Rules	Rule 1	A + A’B = A + B
	Rule 2	A’ + AB = A’ + B
	Rule 3	A + AB = A
	Rule 4	A(A + B) = A
	Rule 5	(A + B)(A + B’) = A