# Binary To Decimal Converter

To find Decimal equivalent of Binary number, enter a Binary number to be converted in the below given text box. Then click on “Click here to Convert” button to get the Decimal value of the given Binary number. This online mixed Binary to Decimal Converter will able to convert 63 digits binary to its decimal equivalent very easily. The Binary Decimal Converter is able to support for both Integer number as well as Real number.

(Enter a Binary Number in the Below given Text Box)

## Binary Number System

The Binary Number System contain only two digits such as 0 and 1. The binary digit 0 represents no information and 1 represents information. AS we know that, the digital computers are designed by using Binary. However, all the electronic circuits are functioned with binary signals. It is clear that he electronic devices are operated by using binary. Technically, the binary 1 indicate a high signal and 0 indicate a low signal. Since the Binary Number System consist of only two digits, the base of Binary Number System is 2. In a Binary number, each digit position has its own weight. The weights of a mixed Binary Number are . . . . 2^{3} 2^{2} 2^{1} 2^{0} . 2^{-1} 2^{-2} 2^{-3} 2^{-4} . . . .

## Decimal Number System

The Decimal Number System contain only ten digits namely 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. As we know that it is an Arabic numbers and are used for common use. Since the Decimal Number System has only ten digits, the base of the Decimal Number System is 10. In a Decimal number, each digit positions are having its own weight. The weights of a mixed Decimal Number are . . . . 10^{3} 10^{2} 10^{1} 10^{0} . 10^{-1} 10^{-2} 10^{-3} 10^{-4} . . . .

### Steps to Convert Binary to Decimal

The simple steps needed to convert the given binary number into its equivalent decimal is as follows. To Convert a Binary number to decimal, we must multiply each digit present in the given Binary number by its weight. Then add the product terms together to make the decimal equivalent. This method is applicable for the conversion of both Integer and real part of Binary. A few examples have been done by using mixed Binary to Decimal Conversion method.

## Binary to Decimal Converter Online

## Examples using Binary Decimal Converter

**Binary to Decimal Conversion Example 1:**

Let us find the decimal equivalent of binary number (10101.0101)_{2} by using Binary to Decimal Converter

Given binary number : (10101.0101)_{2}

Decimal equivalent of the binary number is :

1*2^{4} + 0*2^{3} + 1*2^{2} + 0*2^{1} + 1*2^{0} + 0*2^{-1} + 1*2^{-2} + 0*2^{-3} + 1*2^{-4} = 21.3125

Decimal equivalent of (10101.0101)_{2} is (21.3125)_{10}

**Binary to Decimal Conversion Example 2:**

Let us find the decimal equivalent of binary number (101011.10111)_{2} by using Binary to Decimal Converter

Given binary number : (101011.10111)_{2}

Decimal equivalent of the binary number is :

1*2^{5} + 0*2^{4} + 1*2^{3} + 0*2^{2} + 1*2^{1} + 1*2^{0} + 1*2^{-1} + 0*2^{-2} + 1*2^{-3} + 1*2^{-4} + 1*2^{-5} = 43.71875

Decimal equivalent of (101011.10111)_{2} is (43.71875)_{10}

**Binary to Decimal Conversion Example 3:**

Let us find the decimal equivalent of binary number (111100.11101)_{2} by using Binary to Decimal Converter

Given binary number : (101011.10111)_{2}

Decimal equivalent of the binary number is :

1*2^{5} + 1*2^{4} + 1*2^{3} + 1*2^{2} + 0*2^{1} + 0*2^{0} + 1*2^{-1} + 1*2^{-2} + 1*2^{-3} + 0*2^{-4} + 1*2^{-5} = 60.90625

Decimal equivalent of (111100.11101)_{2} is (60.90625)_{10}

### Binary to Decimal Conversion Chart :

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 |

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