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# Number Systems

## What is Number Systems:-

A number system is a system of writing for expressing numbers. It is the mathematical notation for representing numbers of a given set by using digits or other symbols in a consistent manner. It provides a unique representation to every number and represents the arithmetic and algebraic structure of the figures. It also allows us to operate arithmetic operations like addition, subtraction, and division.

The language we use to communicate with each other is comprised of words and characters. We understand numbers, characters and words. But this type of data is not suitable for computers. Computers only understand the numbers** is called** **number system**.

**Ex :-** The counting numbers (1, 2, 3, …) together with the operations of addition, subtraction, multiplication, and division and the properties they satisfy.

**Different number systems are mentioned below.**

- Decimal number system
- Binary number system
- Octal number system
- Hexadecimal number system

**Decimal Number :-**

In algebra, a decimal number can be defined as a number whose whole number part and the fractional part is separated by a decimal point. The dot in a decimal number is called a decimal point. The digits following the decimal point show a value smaller than one.

Decimals are based on the preceding power of 10. The number system that we follow is called as Decimal Number System where the base is 10.The base 10 indicates that there are 10 different symbols that we use it.

**Ex:-** (**91274934**)10 all base of **10 **is a Decimal number.

**Binary Number :-**

The binary number system is a numbering system that represents numeric values using two unique digits (0 and 1). Mostly computing devices use binary numbering to represent electronic circuit voltage state, (i.e., on/off switch), which considers 0 voltage input as off and 1 input as on. A binary number system is a system which has a base of two. It means that it has only 2 different symbols that make up its number system.

**Ex:- **(**101010001**)2 all base of **2** is binary number.

**Octal Number :-**

An Octal Number System is a number system having eight digits only (0,1,2,3,4,5,6,7). This means any number can be written using the eight digits of this system.

For example, we use the decimal system where there are 10 digits (0,1,2,3,4,5,6,7,8,9) & all numbers are formed using these 10 digits. But for octal system, all numbers will be formed using only eight digits (0,1,2,3,4,5,6,7).

**Ex :- **(**7561235**)8 all base of** 8** are octal number

**Hexadecimal Number :-**

This number system has 16 digits that ranges from 0 to 9 and A to F. So, its base is 16. The A to F alphabets represent 10 to 15 decimal numbers. The position of each digit in a hexadecimal number represents a specific power of base (16) of the number system. As there are only sixteen digits, four bits (24=16) of binary number system can convert any hexadecimal number into binary number. It is also known as alphanumeric number system as it uses both numeric digits and alphabets.

**Ex:-** (**AB190FD**)16 all base of **16** number are Hexadecimal number