In our day-to-day lives we will have to depict/represent certain objects with a quantity. The number system can be defined as the system which uses particular words or symbols for quantifying a given object or value. For example, teachers would grade/assign a particular numerical value to the examination paper depending upon the student’s performance giving us an idea about the knowledge and preparation level of the student.

A number is a word/symbol that represents a certain quantity.

‘Numbers’ have essentially helped us in achieving progress in the field of physics and mathematics.

Numbers are used for basic chores/tasks. For example, money carries a certain value represented by numbers. A person’s contact number is nothing but a bunch of numbers grouped together!

Counting Numbers

Set of numbers used for counting certain objects are called counting numbers.

It starts frome one, goes till infinity.

Used in everyday life for basic exchange, calculations and operations.

The Number Zero

Number zero (0) is assigned to something which has no value at all. It comes before all counting numbers, forming the set of ‘whole numbers’.

There are several types of numbers in the subject of mathematics.

Set of numbers used for counting objects are called natural numbers. They comprise only positive integers, start with 1 and go on till infinity.

Whole numbers are defined as the set of numbers which includes all the positive integers and zero.

An integer is a whole number which can assume either positive, negative or no value at all.

Real numbers comprise both rational and irrational numbers.

Rational numbers can be depicted in the form of a fraction.

We cannot express irrational numbers as a fraction.

There are the following categories of numbers as well,

Numbers which can be divided by 2 are called even numbers. Example: 2, 4, 6 etc ..

Numbers that are not divisible by 2 are called odd numbers. Example: 3, 5, 7 etc ..

Prime numbers can be divided exactly by themselves or 1. Example: 5, 7, 13 etc ..

Composite numbers have multiple factors other than 1 and the number itself. Example: 16, 20, 50 etc ..

Number System

Number system is used to define a set of values, it is used for representing a quantity.

Types of Number Systems

There are different types of number systems in mathematics. The four most common number system types include the decimal number system, binary number system, octal number system, and the hexadecimal number system.

Decimal Number System

The number system has a base value of 10.

Digits ranging from 0-9 are used for the creation of numbers.

Every digit is represented as its product with different powers of 10.

Place value continues to increase from right to left.

Binary Number System

The type of number system has a base value of 2.

In this system, only two digits, i.e, 0 and 1 are used for creating numbers.

Used in computer applications.

For example: 14 can be written as 1110, 50 may be written as 110010.

Octal Number System

The system has a base value of 8.

For example: (112)_{10} can be expressed as (287)_{8}.

Hexadecimal Number System

Having a base value of 16, the system uses 16 digits for the creation of numbers.

For example: (255)_{10} may be written as (FF)_{16}.

(4090)10 can be written as (FF)_{16}.

What is the importance of the number system?

Number system plays a crucial role in our day-to-day lives.

It helps us keep count of things around us.

Enables unique/accurate representation of several types of numbers.

Used for computation in the banking sector.

Helps us in encrypting data, avoiding hacking and misuse of data.

Allows easy conversion of numbers for technical purposes.

It should be noted that every fiber of data gets stored in the computer as a number.