In order to use this new binary to decimal converter tool, type any binary value like 1010 into the first field below, and then hit the Convert button. You can see the result in the right field below. It is possible to convert up to 63 binary characters to decimal.

## Binary to decimal converter

Enter binary value like 1010 and press the *Convert* button:

## 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 System

Binary is the simplest kind of number system that uses only two digits of 0 and 1. By using these digits computational problems can be solved by machines because in digital electronics a transistor is used in two states. Those two states can be represented by 0 and 1. That is why this number system is the most preferred in modern computer engineer, networking and communication specialists, and other professionals.

### Decimal System

Decimal number system is the most commonly used and the most familiar one to the general public. It is also known as Base 10 numbering system since it is based on 10 following symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. In decimal system, every digit has its own position as well as the decimal point. I.e. the number 356.74 has 4 in the Hundredths position, 7 in the Tenths position, 6 in the Units position, 5 in the Tens position, and 3 in the Hundreds position. Decimal number system is also one of the oldest known numeral system, which is historically related to Hindu-Arabic numeral system.

## Binary to decimal conversion table

Binary | Decimal |
---|---|

0 | 0 |

1 | 1 |

10 | 2 |

11 | 3 |

100 | 4 |

101 | 5 |

110 | 6 |

111 | 7 |

1000 | 8 |

1001 | 9 |

1010 | 10 |

1011 | 11 |

1100 | 12 |

1101 | 13 |

1110 | 14 |

1111 | 15 |

10000 | 16 |

10001 | 17 |

10010 | 18 |

10011 | 19 |

10100 | 20 |

10101 | 21 |

10110 | 22 |

10111 | 23 |

11000 | 24 |

11001 | 25 |

11010 | 26 |

11011 | 27 |

11100 | 28 |

11101 | 29 |

11110 | 30 |

11111 | 31 |

100000 | 32 |

1000000 | 64 |

10000000 | 128 |

100000000 | 256 |

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