Boolean Algebra

Boolean algebra is a system of rules for manipulating logic equations, which are expressions that describe logic circuits and the results they produce. It is one of the primary means for applying the reduction technique, which aids in simplifying logic circuits.

AND Operator Symbol

A dot symbol is usually used to represent the AND function.

OR Operator Symbol

The cross symbol usually represents the OR function.

NOT Operator Symbol

The bar symbol over the variable represents the NOT function.

When One Input is Binary 0

• A.0=0
• A+0=A

When One Input is Binary 1

• A.1=A
• A+1=1

When Inputs are the Same

• A.A=A
• A+A=A

When One Input is Inverted

• A.Ā=0
• A+Ā=1

Associative Rules

The associative rule states that the grouping of the variables does not matter.

• A+(B+C)=(A+B)+C
• (A.B).C=A.(B.C)

Commutative Rules

The commutative rule states that the order of operations does not matter.

• A+B=B+A
• A.B=B.A

Distributive Rules

The distributive rule is very useful as it allows the process of factoring. If you are able to factor out a common variable, then the Boolean equation becomes simpler.

• A.(B+C)=(A.B)+(A.C)
• A+(B.C)=(A+B).(A+C)

This Article Continues...