Converting hexadecimal to octal is a common task in computer programming. Hexadecimal is a `base-16`

number system that uses sixteen digits, 0 through 9 and A through F. Octal, on the other hand, is a `base-8`

number system that uses eight digits, 0 through 7. Converting hexadecimal to octal involves converting the hexadecimal number to binary, and then converting the binary number to octal.

## Conversion

Here’s a step-by-step guide on how to convert hexadecimal to octal:

- Choose the hexadecimal number you want to convert to octal.
- Convert the hexadecimal number to binary using the table below.
- Group the binary digits into groups of three, starting from the rightmost digit. If the leftmost group has less than three digits, add leading zeros to make it a group of three.
- Convert each group of three binary digits to its octal equivalent using the table below.
- Write the octal equivalent of each group of three binary digits in order to get the octal representation of the binary number.

## Example

Let’s walk through an example to illustrate the process. Suppose we want to convert the hexadecimal number 2A to octal.

- The hexadecimal number we want to convert is
`2A`

. - We convert the hexadecimal number to binary using the table below: 0010 1010.
- We group the binary digits into groups of three: 000 101 010.
- We convert each group of three binary digits to its octal equivalent using the table below. 000 = 0, 101 = 5, 010 = 2.
- We write the octal equivalent of each group of three binary digits in order to get the octal representation of the binary number: 052.

## Hexadecimal-Binary Table

Hexadecimal | Binary |
---|---|

0 | 0000 |

1 | 0001 |

2 | 0010 |

3 | 0011 |

4 | 0100 |

5 | 0101 |

6 | 0110 |

7 | 0111 |

8 | 1000 |

9 | 1001 |

A | 1010 |

B | 1011 |

C | 1100 |

D | 1101 |

E | 1110 |

F | 1111 |

## Binary-Octal Table

Binary | Octal |
---|---|

000 | 0 |

001 | 1 |

010 | 2 |

011 | 3 |

100 | 4 |

101 | 5 |

110 | 6 |

111 | 7 |