Boolean Algebra Laws and Rules in Digital Electronics | New Topic - Poly Notes Hub
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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
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Boolean Algebra Laws and Rules in Digital Electronics | New Topic - Poly Notes Hub
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