# Binary to Decimal converter

Convert binary numbers to decimal effortlessly with our online tool. Whether you have a binary string or a series of binary digits, our converter can accurately convert it into decimal form. Simply input the binary number and let our converter do the rest. It supports both unsigned and signed binary numbers, providing flexibility for different applications.

## What is Binary to Decimal converter

A Binary to Decimal converter is a tool that allows you to convert binary numbers (base-2) into decimal numbers (base-10). The binary system uses only two digits, 0 and 1, while the decimal system uses ten digits, 0 to 9.

Here's how a Binary to Decimal converter typically works:

- Input the binary number you want to convert.
- Starting from the rightmost digit, assign each digit a positional value of 2 raised to the power of its position (from right to left), starting from 0.
- Multiply each binary digit by its corresponding positional value and sum them up.
- The sum obtained is the decimal equivalent of the binary number.

For example:

- Converting the binary number 1010 to decimal would be calculated as: (1 * 2^3) + (0 * 2^2) + (1 * 2^1) + (0 * 2^0) = 8 + 0 + 2 + 0 = 10.

Binary to Decimal converters are commonly used in computer programming and digital systems analysis. They are available as online tools, calculator applications, or programming language functions for convenient conversion between binary and decimal representations.

## How to convert binary to decimal

For binary number with n digits:

*d _{n-1} ... d_{3} d_{2} d_{1} d_{0}*

The decimal number is equal to the sum of binary digits (d_{n}) times their power of 2 (2^{n}):

decimal = *d*_{0}×2^{0} + *d*_{1}×2^{1} + *d*_{2}×2^{2} + ...

### Example

Find the decimal value of 111001_{2}:

binary number: | 1 | 1 | 1 | 0 | 0 | 1 |
---|---|---|---|---|---|---|

power of 2: | 2^{5} |
2^{4} |
2^{3} |
2^{2} |
2^{1} |
2^{0} |

111001_{2} = 1⋅2^{5}+1⋅2^{4}+1⋅2^{3}+0⋅2^{2}+0⋅2^{1}+1⋅2^{0} = 57_{10}

## Binary to decimal conversion table

Binary Number |
Decimal Number |
Hex Number |
---|---|---|

0 | 0 | 0 |

1 | 1 | 1 |

10 | 2 | 2 |

11 | 3 | 3 |

100 | 4 | 4 |

101 | 5 | 5 |

110 | 6 | 6 |

111 | 7 | 7 |

1000 | 8 | 8 |

1001 | 9 | 9 |

1010 | 10 | A |

1011 | 11 | B |

1100 | 12 | C |

1101 | 13 | D |

1110 | 14 | E |

1111 | 15 | F |

10000 | 16 | 10 |

10001 | 17 | 11 |

10010 | 18 | 12 |

10011 | 19 | 13 |

10100 | 20 | 14 |

10101 | 21 | 15 |

10110 | 22 | 16 |

10111 | 23 | 17 |

11000 | 24 | 18 |

11001 | 25 | 19 |

11010 | 26 | 1A |

11011 | 27 | 1B |

11100 | 28 | 1C |

11101 | 29 | 1D |

11110 | 30 | 1E |

11111 | 31 | 1F |

100000 | 32 | 20 |

1000000 | 64 | 40 |

10000000 | 128 | 80 |

100000000 | 256 | 100 |