Boolean Algebra:
Boolean algebra derives its name from the mathematician George Boole. Symbolic Logic uses values, variables and operations :
- True is represented by the value 1.
- False is represented by the value 0.
Variables are represented by letters and can have one of two values, either 0 or 1. Operations are functions of one or more variables.
- AND is represented by X.Y
- OR is represented by X + Y
- NOT is represented by X' . Throughout this tutorial the X' form will be used and sometime !X will be used.
Boolean Addition:
The basic rules for Boolean addition are as follows:
0+0 = 0
0+1 = 1
1+0 = 1
Note: Boolean addition is same as the OR operation.
Boolean Multiplication:
0.0 = 0
0.1 = 0
1.0 = 0
1.1 = 1
Note: Boolean multiplication is same as the AND operation.
Boolean Laws:
The following are the Boolean Rules:
Commutative Law:
Associative Law:
Distributive Law:
AND and OR Laws:
De Morgan's Theorem:
The most important logic theorem for digital electronics, this theorem says that any logical binary expression remains unchanged if we
- Change all variables to their complements.
- Change all AND operations to ORs.
- Change all OR operations to ANDs.
- Take the complement of the entire expression.
