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Number System in math and Computer: Definition, Types

Number System is the basic and first fundamental of Mathematics. Each person who starts learning mathematics must have a basic knowledge of the numbers. In this topic, you will learn Number System in Math and computer Number system types with examples.


Number System Introduction

What is the Number System?

The number system is nothing but a systematic procedure to represent one or number in a proper manner or you can say that the number system is set of all the possible numbers.

You will find the concept of the number system in two different education systems. These are:

  1. Number System in Math
  2. Number System in Computer

Let us Discuss one by one in detail.

Number System in Math

Number Systems in Math is a vast topic. But it’s very important for all the students who want to score good marks in mathematics. There are 5 types of Numbers. Such as: 

  1. Natural Numbers
  2. Whole Numbers
  3. Integers
  4. Rational Numbers
  5. Irrational Numbers
  6. Real Numbers

1) Natural Numbers

First of all, carefully see the number line  given below:



As you can see in the number line, from zero points to onward you will find only positive numbers. These are called Natural Numbers.

It is denoted by the symbol ‘N’.

The numbers that we used for our counting are called Natural Numbers. Examples of Natural Numbers
1, 2, 3, 4, 10, 123, 1456, 96565, …

2) Whole Numbers

In the above figure, we saw that all the positive numbers are known as Natural Numbers. But zero (0) is not included in the Natural number list.

If we will add Zero to the Natural list, then the list of Numbers is called Whole Numbers.

It is denoted by ‘W’ symbol.





Examples of Whole Number
0, 1, 2, 3, 620,2652, …..

3) Integers

Still, now we have discovered Natural Numbers and Whole numbers. But there are negative numbers which need to be grouped.

The combination of whole numbers and all negative numbers from the number line are called Integers.

It denoted by the letter ‘Z’.




Examples of Integers
-1, -2, -3, -4 -556, -555, 0, 1, 2, 3, 620,2652, …..

4) Rational Numbers

Do you think all the numbers have been grouped? No, not at all. There are some numbers which in the number line, but not included in all the above groups.




As you can see in the above number line in between each integer there are the infinite numbers in decimal numbers in p/q format. These numbers are called Rational Numbers.

Any integers in p/q format are called Rational Numbers where q ≠ 0 and p & q are two integers.

It is denoted by the Symbol ‘Q’.

Examples of Rational Number
1, 1/2, -1/2, 3/2, 3, -5, 30/17, 45/1, -88/1 ….

5) Irrational Numbers

As of now, we have learned all rational numbers are in the form p/q. But there is some number which is not in the form of p/q. These numbers are called Irrational numbers.

In the number system, the numbers which are not in the p/q form are called Irrational Number.

It is denoted by the symbol Q’.

Examples of Irrational Number
√2, √3, √5, π, …

6) Real Numbers

Real Numbers is the set or combination of Rational number and Irrational Numbers.

It is denoted by the symbol ‘R’.

Examples of Real Numbers
1, 2, 0, 1/2, -1, -1/2, √2, √3, √5, π, …

Number System in Computer

Human beings can understand any type of Number system and Mathematics where the computer only can understand Positional number systems.

In this number system, a number is defined as the collection of counting digits.

A number has two parts: Integer and Fraction, both are separated by a radix point (.). Each value of the Integer part and fraction part contain some weight depending upon the position.

Generally in the Computer number system, we use 4 types of Numbers. These are: 

  1. Binary Numbers
  2. Octal Numbers
  3. Decimal Numbers
  4. Hexadecimal Numbers

1) Binary Number System

The binary number system has 2 digits 0 and 1 for representation. It is used in digital electronics, digital computer, and microprocessors as machine level language. 

Examples of Binary Numbers
10, 1010, 1000101, 101001001, …

2) Octal Number System

The Octal Number system uses eight digits. They are 0, 1, 2, 3, 4, 5, 6, 7. It has base number 8. This system is a more convenient way of grouping binary numbers and makes it easier to read.

Examples of Octal Number
17. 56, 176…

3) Decimal Number System

The Decimal Number system is a positional number system. The base of this number system is 10 and we use 10 types of symbols to represent this. They are: 0, 2, 3, 4, 5, 6, 7, 8, 9

Examples of Decimal Numbers
10, 16, 156, …

4) Hexadecimal Number System

Hexadecimal numbers having base 16. It has 16 unique symbols to represent. They are 0, 1, 2, 3, 4….10, A, B, C, D, E, F. It is also known as an alphanumeric number system.

Examples of Decimal Numbers
1233B, B5632, E1, …

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