How to simplify Boolean algebra?

Complex combinational logic circuits must be reduced without changing the function of the circuit.

Reduction of a logic circuit means the same logic function with fewer gates and/or inputs.

The first step to reducing a logic circuit is to write the Boolean Equation for the logic function.

The next step is to apply as many rules and laws as possible in order to decrease the number of terms and variables in the expression.

To apply the rules of Boolean Algebra it is often helpful to first remove any parentheses or brackets.

After removal of the parentheses,common terms or factors may be removed leaving terms that can be reduced by the rules of Boolean Algebra.

The final step is to draw the logic diagram for the reduced Boolean Expression.

What are the Boolean algebra’s rules?

Basic Laws and Proofs. The basic rules and laws of Boolean algebraic system are known as “Laws of Boolean algebra”.

Associative Law.

Distributive law.

Commutative law.

Absorption Law.

Duality Principle in Boolean algebra.

De Morgan’s Theorem.

Consensus Theorem.

Shannon’s Expansion Theorems.

Shannon’s Reduction Theorems.

What are the rules for Boolean algebra?

Boolean algebra rules include Boolean laws as well as Boolean identities and properties that are similar to those in algebra. As Boolean algebra is based on only two values, namely 0 and 1, any Boolean expression can be solved using a truth table, wherein each variable in the expression is assigned the values 0 and 1.

What are the basic theorems of Boolean algebra?

Boolean Algebraic Theorems DE Morgan’s Theorem represents two of the most important rules of boolean algebra. Transposition Theorem : This theorem is used to eliminate the redundant terms. Duality Theorem : Dual expression is equivalent to write a negative logic of the given boolean relation. Complementary Theorem : Change each OR sign by AND sign and vice-versa.