**Let’s Learn About Number System and Its Types**

Mathematical values are always required for counting and measuring objects and for Performing various arithmetic calculations. Numbers can be divided into various categories like the whole number, rational number, irrational number, decimal number, and so on therefore, we can divide the number systems into different types which have many different properties. For example The Decimal __number system__, The Binary Number System, The Octal Number System, The hexadecimal Number System, etc.

**Significance of Number System**

A system that represents numbers is called a number system. A number system is also known as a system of numeration. This can be defined as a set of values to represent a quantity. numbers can be used as digits and in the form of ones are 0 and 1 which are used in the binary number system. However, numbers from 0 to 9 are used to represent other types of number systems. These concepts can also be learned online from platforms like cuemath.com.

#### Number System Definition

**T**he representation of numbers by using the digits or other symbols in a constant manner is called the Number system. Its value can be expressed by any digits in the number and its location present in the number, and the base of the Number system. The numbers are always expressed in a constant manner and allow us to operate arithmetic operations such as estimation, addition, subtraction, multiplication division, and many other arithmetic operations.

**Various Types of Number System**

Many types of Number Systems occur in Maths, in which these four are most common**.**

*****Binary Number System (Base-2)

*Decimal Number System (Base-10)

*Hexadecimal Number System (Base-16)

*Octal Number System (Base-8)

**Binary number system **– A method of mathematical expression which uses two symbols which are zero ”0” and “1”. It can also be represented by a sequence of bits because it is used in digital electronic circuits using logic gates. All modern computers and computer-based devices are commonly used binary systems. Arithmetic in binary is most like arithmetic in comparison to other numeral systems.

**Decimal number systems – **Those number systems which have 10 base values are called decimal number systems. It plays the most important role in the development of science and technology. In this system, the value of each digit is expressed by its position in a number. It is also known as the base-10 number system. Each position in this system is 10 times more significant than the previous position. For Example- The number 4025 is interpreted as-

Here, rightmost bit 5 is the least significant bit and left most bit 4 is a most significant bit

**Hexadecimal number system **-Those number systems that have 16 base values are called hexadecimal number systems. Hexadecimal uses 16 distinct symbols, these are widely used by computer system designers and programmers. Each hexadecimal digit represents four bits also known as a nibble. The hexadecimal number system has digits from 0 to 9 and from 10-16 they are represented in symbols. i.e.,10 as A,11 as B,12 as C,13 as D,14 as E,15 as F.

For example -(28E)16(28E)16, (AC7)16(AC7)16 are all hexadecimal numbers.

**Octal number system – **As the number suggests whose base is eight (8) is known as the Octal Number system and this system uses the digits from 0 to 7. In this number system, all digits 0 to 7 have the same physical meaning as that of other number systems. But there is a disadvantage of this number system is that our operating system or Computer doesn’t understand this Octal Number System. As we know, Binary Number System is required for Computers. So, we must add another digital circuit that converts octal numbers to Binary numbers. One of the examples of conversion is –

#### Use of Place Value in Number System

We can explain the place value in the number system in the following way: In __place value__, each digit has a specific place. For example, the 6 in 960 represents 6 tens or 60, 9 in 9867 represents 9 thousand, and 7 in 87 represents only 7 because it has the last unit place. With the help of the place value of digits, we can write the expanded form in a digit.

For example: 5789 is 5000+700+80+9

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