# Base Converter

Convert numbers between different numeral systems effortlessly. Our user-friendly online tool supports the conversion of numbers between various bases, including binary, decimal, octal, and hexadecimal. Easily convert your numbers from one base to another with a simple input and get accurate results instantly.

## What is Base Converter

A Base Converter is a tool that allows you to convert numbers from one numeral system (or base) to another. It supports conversions between various bases such as decimal (base-10), binary (base-2), hexadecimal (base-16), octal (base-8), and more.

Here's how a Base Converter typically works:

- Input the number you want to convert and specify its original base.
- Select the target base you want to convert the number into.
- The tool will convert the number from its original base to the target base and provide the result.

For example:

- Converting the decimal number 10 to binary would yield 1010.
- Converting the binary number 1011 to hexadecimal would yield B.

Base Converters are useful for a variety of purposes, including computer programming, digital systems, mathematics, and cryptography. They can be found as online tools or integrated into software applications for easy and convenient conversions between different numeral systems.

## How to convert from any base to any base

- Convert from source base to decimal (base 10 ) by multiplying each digit with the base raised to the power of the digit number (starting from right digit number 0):

decimal = β(digitΓbase^{digit number}) - Convert from decimal to destination base: divide the decimal with the base until the quotient is 0 and calculate the remainder each time. The destination base digits are the calculated remainders.

## Base Converter Example

Decimal | Binary | Octal | Hexadecimal |
---|---|---|---|

0 | 0 | 0 | 0 |

1 | 1 | 1 | 1 |

2 | 10 | 2 | 2 |

3 | 11 | 3 | 3 |

4 | 100 | 4 | 4 |

5 | 101 | 5 | 5 |

6 | 110 | 6 | 6 |

7 | 111 | 7 | 7 |

8 | 1000 | 10 | 8 |

9 | 1001 | 11 | 9 |

10 | 1010 | 12 | A |

11 | 1011 | 13 | B |

12 | 1100 | 14 | C |

13 | 1101 | 15 | D |

14 | 1110 | 16 | E |

15 | 1111 | 17 | F |

In this table, the "Decimal" column represents the decimal numbers, while the other columns represent their respective base representations: binary, octal, and hexadecimal.

For example:

- The decimal number 5 corresponds to binary 101, octal 5, and hexadecimal 5.
- The decimal number 10 corresponds to binary 1010, octal 12, and hexadecimal A.

You can use this table as a reference to convert numbers between different bases by finding the corresponding representation in the desired base.