TABLE OF CONTENTS This chapter begins with the basic logic operations and continues with the fundamentals of Boolean algebra and the basic postulates and theorems as applied to electronic logic circuits. Truth tables are defined and examples are given to illustrate how they can be used to prove Boolean algebra theorems or equivalent expressions.
The following three logic operations constitute the three basic logic operations performed by a digital computer.
Conjunction (or logical product) commonly referred to as the AND operation and denoted with the dot (.) symbol between variables.
Disjunction (or logical sum) commonly called the OR operation and denoted with the plus (+) symbol between variables
Negation (or complementation or inversion) commonly called NOT operation and denoted with the bar ( ?) symbol above the variable.
This section introduces the basics of Boolean algebra. We need to know these to understand Chapter 6 and all subsequent chapters in this text.
Postulates (or axioms) are propositions taken as facts; no proof is required. A well-known axiom states that the shortest distance between two points is a straight line.
Let X be a variable. Then, X= 0 or X=1. If X=0, then X=1, and vice-versa.
0 0=0
0 1=1 0=0
1 1=1
0+0=0
0+1=1+0=1
1+1=1
Commutative laws
A B=B A
A+B=B+A
Associative laws
(A B) C=A (B C)
(A+B)+C=A+(B+C)
Distributive laws
A (B+C)=A B+A C
A+(B C)=(A+B) (A+C)
Identity laws
A A=A
A+A=A
Negation laws
(A)= A
= 
=A
Redundancy laws
