# Octal To Decimal Converter

_{8}

_{10}## How to convert a octal number to the decimal number?

Converting an octal number to decimal is a straightforward process where each octal digit is treated as a positional value in base-8 and then summed up. In octal, each digit represents powers of 8. **Begin by understanding the positional values of each digit**, with the rightmost digit representing **8 ^{0}**, the next

**8**, and so on. Replace each octal digit with its decimal equivalent:

^{1}**Convert each octal digit to its decimal equivalent**and multiply it by the corresponding positional value. Sum up these products to obtain the decimal equivalent of the entire octal number. This method provides a clear step-by-step approach for manual conversion, allowing for a better understanding of the positional values associated with each octal digit.

For **d** number of octal digit.[where **n = 1,2,3...** is positon of that digit.]:

d_{n-1} .... d_{4} d_{3} d_{3} d_{2} d_{1} d_{0} **.** d_{-1} d_{-2} d_{-3}

The decimal number is equal to the sum of octal digits (d_{n}) times their power of (8^{n}):

decimal = *d*_{n-1} x 8^{n-1} + .... + *d*_{1} x 8^{1} + *d*_{0} x 8^{0} + *d*_{-1} x 8^{-1} + .... + *d*_{-n} x 8^{-n}

### Example of octal to decimal conversion.

(57.62)_{8} = (?)_{10} or make a conversion binary to decimal.

octal number: | 5 | 7 | . | 6 | 2 |
---|---|---|---|---|---|

power of 8: | 8^{1} |
8^{0} |
8^{-1} |
8^{-2} |

(57.62)_{8}= (?) _{10}

= 5 x 8^{1} + 7 x 8^{0} + 6 x 8^{-1} + 2 x 8^{-2}

= 40 + 7 + 0.75 + 0.03125

= (47.78125)_{10}

### Binary to decimal conversion table:

Octal | Decimal |
---|---|

0 | 0 |

1 | 1 |

2 | 2 |

3 | 3 |

4 | 4 |

5 | 5 |

6 | 6 |

7 | 7 |

10 | 8 |

11 | 9 |

12 | 10 |

13 | 11 |

14 | 12 |

15 | 13 |

16 | 14 |

17 | 15 |

20 | 16 |

21 | 17 |

22 | 18 |

23 | 19 |

24 | 20 |