# Number System :-

The number system is defined as the way for representing the values in digital world ,there are mainly 4 types of number system which is mostly used in various computer and digital studies.

# Types of number System :-

- Decimal Number System
- Binary Number System
- Octal Number System
- Hexadecimal Number System

**1)
Decimal Number System :-**

The decimal number system is use in our daily life in mathematical calculations and in almost every calculation criteria, it consist of the number starting from 0 to 9.

Its base or radix is 10 because it contain 10 numbers they are

0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9

For example the number 654321 then

6 is on lack
(10^{5}) place, 5 is on ten thousand^{th}(10^{4})
place, 4 is on thousand^{th}(10^{3}) place, 3 is on hundred^{th}
(10^{2}) place, 2 is on tens (10^{1}) place and 1 is on zero
(10^{0}) place.

Note that 10^{0}
= 1, 10^{1} = 10 , 10^{2} = 100 , 10^{3} = 1000 , 10^{4}
= 10,000 , 10^{5} = 1,00,000

**2) Binary
Number System :-**

The binary number system is usually use in computer’s machine language, it is also called machine friendly language, In this number system only two numbers 0 & 1 are used for calculating any other binary number.

Its base or radix is 2 because it contain only 2 numbers which are

0 , 1

For example
the number 101010 have values 2^{0} = 1, 2^{1} = 2 , 2^{2}
= 4 , 2^{3} = 8 , 2^{4} =16 , 2^{5} = 32

**3) Octal Number
System :-**

The octal number system consist of the number starting from 0 to 7

Its base or radix is 8 because it contain8 numbers which are

0 , 1 , 2 , 3 , 4 , 5 , 6 , 7

For example
the number 76345 have values 8^{0} = 1, 8^{1} = 8 , 8^{2}
= 64 , 8^{3} = 512 , 8^{4} =4,094

**4) Hexadecimal
Number System :-**

The word hexadecimal is made with the combination of two words “hexa” means 6 and “Decimal” means 10 which means the number system which contain 16 digits, it is so compact number system .

Its base or radix is 16 because it contain 10 numbers and 6 alphabets which are

0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , A , B , C , D , E , F

In which A , B , C , D , E , F has values 10 , 11 , 12 , 13 , 14 , 15