Terminology of Boolean Expressions

A Boolean expression has the following terms

Literals

A literal is a single Boolean variable or it's complement

Constant

A constant is a value or the quantity which has a fixed (unchanging) value. In real number (conventional) algebra, constants include all integers and fractions. In Boolean Algebra, there are only two possible constants 1 and 0. These two constants are used to describe true and false, YES or NO, etc.

Variable

A variable is a quantity which can change its value by taking on the value of any constant. At any one itme the variable has only one particular value of constant. There are only two values of constants in the Boolean System. Therefore, a variable in Boolean algebra can only be either 0 or 1. Variables are denoted by letters.

Term

A term is a literal or a collection of literals.

Product Term

A product ( logical AND) of several different literals is called the product term. For example :

A.B' is a product term

Sum Term

The Logical OR of Literals is called the sum term. For example:

A+B'+C

is an example of sum term

Sum of Products

It is the sum (logical OR) of product terms. For example 

A.B' +B.C + A.B.C

is the sum of three different erms i.e. A.B', B.C and A.B.C

Product of Sum

It is tthe product (logical AND) of sum terms. For example:

(A+B).(A+B'+C).(A+C)

is the product of three different sum terms i.e. (A+B), (A+B'+C) and (A+C)

Minterm

A minterm is an AND function that includes each variable once in its normal or complemented form. This is also known as the standard sum of products. For example:

If you have two variables, A and B, there are eight possible terms:

A, B, A', B', A'B', A'B, AB' and AB.

Similarly for three variables we have 26 possible terms.

Maxterm

A maxterm is a logical OR function that includes each variable once in its normal or complemented form. This is known as standard product of sums.

Boolean Algebra : Truth Table

A truth table is a table in which the truth or falsity of a statement is listed for all possible proposition conditions. A truth able lists the value of the dependent variable for each set of values of the independent variables. Suppose there are three variables C, A and B, wherein the variable C is being derived from some expression based on the variables A and B.

Then, C is called the dependent variable because i is dependent on and being derived from A and B. Variables A and B are independent variables because they do not depend on any thing. So, in this example, preparing a truth table means deriving the value for dependent variable i.e. C for each set of values of independent variables (A and B).

Bu in Boolean algebra any variable can have only two values i.e. 0 and 1.

So A and B can only have values 0 and 1.

together they can have 4 possible combinations of 0 and 1 as follows.

Table 1 : Possible values of A and B

              A                B

              0                 0

              0                 1

              1                 0

              1                 1

Calculating the value for C for each possible set of values of A and B is called the Truth Table.

Table 2 : Truth able for values of A, B, and C

              A                B               C

              0                 0                0

              0                 1                0

              1                 0                0

              1                 1                1

Boolean Algebra : Binary Valued Quantities

What we think of in our daily life involves finding answer to two valued questions: like "Is the action RIGHT or WRONG"? Is this statement TRUE or FALSE?

Such type of decision statements which result in YES or NO, RUE or FALSE. RIGHT or WRONG are binary decisions. In electronics it is used in addition to describe circuits whose state can be either 1(true) or 0 (false). Two-state logic or proposition had a major influence on Aristotle, who worked out precise methods for getting to the truth.

Then Augustus de Morgan found the link between logic and mathematics. But it was George Boole who invented a new kind of algebra by putting it all together. therefore it is known as Boolean Algebra.

Boolean Algebra is he algebra of binary variables. Binary variables are also known as Boolean Variables. Boolean variable can have only two values, 0 and 1. he mathematical operations available are AND, OR, and NOT.

Boolean Algebra : Introduction

Boolean pronounced as booln is an abstract mathemetical sysem primarily used in expressing the relationships between sets(groups of objects). The English mathemtician George Boole developed this notational system. Such manipulation can demonsrate whether or not a statement is true and show how a complicated statement can be rephrased in a simpler, more convenient form without changing its meaning.

The phrase Boolean operators refer to the system of logic developed by George Boole. The so-called operators are AND, OR, and NOT and more recently terms such as NEAR, IN, and ADJ have been added to the list.

They represent logical ways of combining concepts, words, and ideas. Boolean operators if used in a search statement either narrow, expand, or limit the search result. Two of the most powerful operators are NEAR and ADJ.

NEAR when used between two words means that those words are found near each other in the records

ADJ means that two words are found next to each other in the records.

AND results in key words being located seperately in different documents.

There is a tenuous relationship between Boolean functtions and Boolean expressions in programming languages like C or Pascal.

However the relationship between Boolean Logic and computer systems is much stronger.

There is a one-to-one relationship between Boolean functions and electtronic circuits.