Integrated Circuits (ICs) are compact electronic circuits that integrate multiple components into a single chip. In this article, we are going to discuss Axioms of Boolean Algebra; these axioms/Theorems are important as these will be used in many different topics of Digital Electronics like Sequential Circuit Designing and Combinational Circuit Designing as well. These Axioms are the building blocks of Digital Electronics. Now we will look into these Axioms one by one.
Integrated Circuits
These generalized expressions are very important as they are used to simplify many Boolean Functions and expressions. Minimizing the boolean function is useful in eliminating variables and Gate Level Minimization. View all O’Reilly videos, virtual conferences, and live events on your home TV. O’Reilly members experience books, live events, courses curated by job role, and more from O’Reilly and nearly 200 top publishers. There are also live events, courses curated by job role, and more.
Axioms of Boolean Algebra:
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- A Boolean function is an expression formed using binary variables, logical operators (AND, OR, NOT), and constants (0, 1).
- The sets of logical expressions are known as Axioms or postulates of Boolean Algebra.
An axiom is nothing more than the definition of three basic logic operations (AND, OR, and NOT). A Boolean function is an expression formed using binary variables, logical operators (AND, OR, NOT), and constants (0, 1). Using simple properties of integers and of l.c.m. and h.c.f. we can easily show that axioms (1)-(3) given in the definition of a Boolean algebra are satisfied. Now axiom (4) will hold if and only if for any a ϵ B, a and n/a have no common factor, other than 1. This condition is equivalent to n being square-free.
- These Axioms are the building blocks of Digital Electronics.
- This condition is equivalent to n being square-free.
- If these axioms as; Commutative, Associative, Distributive, Idempotence, and Absorption are learned, complicated Boolean expressions can be simplified and this results in efficient circuit designs.
- An axiom is nothing more than the definition of three basic logic operations (AND, OR, and NOT).
- Using simple properties of integers and of l.c.m. and h.c.f. we can easily show that axioms (1)-(3) given in the definition of a Boolean algebra are satisfied.
Complement Property
Therefore it can be inferred that Boolean Algebra in its axioms and theorems acts as the basis on which digital electronics mainly builds sequential and combinational circuits. If these axioms as; Commutative, Associative, Distributive, Idempotence, and Absorption are learned, complicated Boolean expressions can be simplified and this results in efficient circuit designs. This is opposed to arithmetic algebra where a result may come out to be some number different from 0 or 1 showing the binary nature of Boolean operations and confirming that Boolean axiomatic definition of boolean algebra logic is distinctive in digital systems. The sets of logical expressions are known as Axioms or postulates of Boolean Algebra.