In Mathematics, a number system is a form of representing numbers in a digital system. These numbers are binary numbers, octal numbers, decimal numbers and hexadecimal numbers. These numbers are represented by using digits or symbols.

A number has numerous different varieties, for example, even and odd numbers, prime and composite numbers. Indeed, even and odd terms are utilized when a number is detachable by 2 or not, though prime and composite separate between the numbers that have just two elements and multiple variables, individually.

In a number framework, these numbers are utilized as digits. 0 and 1 are the most well-known digits in the number framework, that are utilized to address paired numbers. Then again, 0 to 9 digits are likewise utilized for other number frameworks. Allow us to learn here the sorts of number frameworks.

## Classification of Number System

As discussed above, the four number systems are:

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

### Binary number system

The base 2 number framework is otherwise called the Binary number framework wherein, just two twofold digits exist, i.e., 0 and 1. In particular, the typical base-2 is a radix of 2. The figures depicted under the binary number system are a mix of 0 and 1. Examples of binary numbers are 1010, 100101, 111010, etc.

### Octal Number System

Octal Number System is one the sort of Number Representation methods, with a base of 8. That implies there are just 8 images or conceivable digit esteems, there are 0, 1, 2, 3, 4, 5, 6, 7. It requires just 3 pieces to address the estimation of any digit.

Octal Number | Binary Equivalent |

0 | 000 |

1 | 001 |

2 | 010 |

3 | 011 |

4 | 100 |

5 | 101 |

6 | 110 |

7 | 111 |

### Decimal Number System

If the base of the number system is 10, then it is called the Decimal number framework which has the most significant part in the improvement of science and innovation. This is the weighted (or positional) number portrayal, where the estimation of every digit is dictated by its position (or weight) in a number. This is otherwise called the base-10 number framework which has 10 images, these are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

### Hexadecimal Number System

Hexadecimal Number System is one the kind of Number Representation procedures, in which the estimation of base is 16. That implies there are just 16 images or conceivable digit esteems, there are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F. Where A, B, C, D, E and F are single piece portrayals of decimal worth 10, 11, 12, 13, 14 and 15 separately.

### Conclusion

As you probably are aware decimal, paired, octal and hexadecimal number frameworks are positional worth number frameworks. In number system conversion, we learn to convert the number, say, a binary number to its equivalent decimal number or octal number or hexadecimal.

Like if we convert a decimal number into a binary number, we need to divide the given number by 2, every time, unless we get 0 as a remainder.

Example: Converting 43_{10} into its binary equivalent, we get,

43_{10} = 101011_{2}

In the same way, the conversion of the number system can be done.