Binary and Decimal Number System





Decimal Number System:

The number of base or radix 10 is called decimal numbers. It is a first number system in which all the ancient and modern mathematical calculation is done. Other number of systems is derived from it.

Our daily life transaction is done in decimal system. There are many number systems available from which we study only decimal, octal, hexadecimal, and binary systems.

The following chart displays relation amongst several number systems:

Decimal Number System

Decimal Number System

 

Binary Number System

Binary number is a number of base (radix) 2. It is represented by 1 and 0.1 or 0 is called BIT (Binary digit). These numbers represents two logical conditions of human life- (A) TRUE, and (B) FALSE. This logic has no any intermediate conditions like fuzzy logic.

Fuzzy logic is applied in artificial intelligence for expert system, and it is a superset logic dealing with concept of partial truth (probability). It was introduced first time in 1960 by Dr. Lottis Zadeh of UC Berkeley.

Sn.

Examples

True

False

1.

Bulb

When switch ON and it delivers light called TRUE condition. When switch OFF and it Delivers no light called FALSE condition.
2.

Engine

If it is started, TRUE condition.

If it is not started FALSE condition.
3. Computer system If it is working properly, TRUE condition. If it is not working properly, FALSE condition.
4.

Human Body

If respiration occurs, TRUE condition.

If no respiration, FALSE condition.

 

In this way, there are many example of TRUE and FALSE in our daily life. Generally, these conditions are working unit of computer or any logic circuit or systems. The machine languages are written in binary numbers. The disciple of Charles Babbage, daughter of English poet Bayron, Lady Ada Agusta, and first time used binary numbers for Programming.

Leibniz (1646-1716) was great advocates of the binary system, according to him 1 represent God and 0 for void. The binary system is ideal for reliable compact storage. The first person known to have used binary codes for number representation was Francis Bacon in 1623.

Decimal

Binary

0

0

1

1

2

10

3

11

4

100

5

101

6

110

7

111

8

1000

9

1001



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