Introduction To Boolean Logic Circuits : Part 1

What is Boolean logic ? And why do we need it ? To understand making logic circuits , first we need to know what is Boolean Algebra ?

BOOLEAN ALGEBRA

Boolean algebra also know as ' Switching Algebra ' is a symbolic analysis of relay switching circuits.

It is represented in Binary Quantities , that in either YES or NO , 1 or 0 , TRUE or FALSE , ON or OFF.

statements  which can be determined to be true or false are called logical statements or truth functions and the results TRUE or FALSE are called truth values. The truth values are depicted by logical constants TRUE and FALSE or 1 and 0. 1 means TRUE and 0 means FALSE. And the variables which can store these truth values are called logical variables or binary valued variables as these can store one of the two values TRUE or False.

Till now you may have understood what is Boolean algebra now we come to how to make truth tables.

TRUTH TABLE

A Truth Table is a table which represents all the possible values of logical variables / statements along with all the possible results of the given combinations of values.

For example, consider a single 2-input logic circuit with input variables labelled as A and B. There are "four" possible input combinations or 2² of "OFF" and "ON" for the two inputs. However, when dealing with Boolean expressions and especially logic gate truth tables, we do not general use "ON" or "OFF" but instead give them bit values which represent a logic level "1" or a logic level "0" respectively.

Then the four possible combinations of A and B for a 2-input logic gate is given as:

Input Combination 1. - "OFF" - "OFF" 

or (0,0)

Input Combination 2. - "OFF" - "ON" or

(0, 1)

Input Combination 3. - "ON" - "OFF" or

(1,0)

put Combination 4. - "ON" - "ON" or

(1,1)

If the result of any logical state ment or expression is always TRUE or 1 for all input combi nations, it is called Tautology.

If the result of any logical statement or expression is always FALSE or 0 for all input combinations, it is called Fallacy.

Now comes the logic operators

LOGIC OPERATORS

There are some specific operations that can be applied on truth functions. Before learning about these operations, you must know about compound logical functions and logical operators.

Logic statement s are combined and written with the help of Logical Operators like 

AND

OR 

NOT 

NAND 

XOR 

NOR

to form compound statements or logical functions.

Here we will learn about the three main operators :-

NOT OPERATOR

This operator operates on single variable and operation performed by NOT operator is called complementation and the symbol we use for it is (bar). Thus (A dash) means complement of A . Here A dash = Y

The truth table of NOT gate is as follows:-

 OR OPERATOR 

A second important operator in boolean algebra is OR operator which denotes operation calle logical addition and the symbol we use for it is +. The + symbol, therefore, does not have the normal' meaning, but is a logical addition or logical OR symbol. Thus A + B can be read a A OR B. (Here represented by Y )

For OR operation the possible input and output combinations are as follows:

AND OPERATOR

AND operator performs another important operation of boolean algebra called logical multi plication and the symbol for AND operation is (.) dot. Thus A. B will be read as A AND B ( here represented by Y )

The truth table for AND is as follows:

So these were the main three operators .

In the next session we will get to know about more other operators and we will start logic gates, to know the remaining portions follow us!

Part 2 :

Introduction To Boolean Logic : 02

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