# HEX to Octal

Hexadecimal, octal, decimal, and binary are the four sorts of number systems we encounter in the number system. These numbers can be transformed from one form to another. We must first convert hexadecimal to its corresponding decimal number before changing decimal to octal to convert hexadecimal numbers to octal numbers. Review the fundamental definitions of hexadecimal and octal numbers before beginning this conversion.

## Conversion of Hexadecimal To Octal

There are four primary sorts of number systems that you may encounter while learning the number system. Hexadecimal, octal, decimal, and binary number systems make up most of these number representations. It is possible to convert between different decimal systems. How are we supposed to convert? A hexadecimal number can be converted to an octal number in two easy steps: first, you need to convert the hexadecimal number to its decimal counterpart, and then you need to convert this decimal value to an octal decimal number. An extensive description of how to convert such numbers can be found in this article.

## What Are Hexadecimal Numbers?

Base-16 numbers, or hexadecimal numbers, are those. 16 distinct digits represent the numbers. The hexadecimal value h16 defines it. It could consist of both letters and numbers. Thus, it has the letters A to F and the digits 0 to 9.

## What are Octal Numbers?

The base of octal numbers is 8. These numbers are known as octal numbers because they have 8 digits, ranging from 0 to 7. The bottom of the octal numbers is 8. The symbol for it is o8, where o is an octal number. It does not represent a number with the digits 8 and 9.

## How to convert hexadecimal numbers to octal?

A hexadecimal number cannot be converted to an octal decimal number. The hexadecimal number must first be converted to its decimal equivalent, which must then be converted to an octal decimal number. The actions listed below can help you comprehend better.

Hex to decimal conversion comes before hex to octal conversion. You can then change the number from decimal to octal.

### Initial step: Hex to Decimal conversion

- From the rightmost number to the left, multiply each digit in the hex number by 16 to the power of n, where n is the distance from the right, to convert the number from hex to decimal.
- The digit farthest to the right when reading a hex number from right to left is equivalent to that digit multiplied by 160. The number multiplied by 161 equals the digit in the first position to the right.
- Number 10 in decimal form is (d0 160) + (d1 161) +... + (dn - 1 16n - 1).
- The hex digit in the formula above that is furthest to the right is d0, the one place to the right is d1, and the digit that is farthest to the left is dn - 1.

### Second step: change decimal to octal

- Divide the decimal number by 8 using long division to convert it to octal. Write the residual, which should range from 0 to 7, to the side of the division issue.
- Divide the answer to the first division puzzle by 8 once more. There should be a residual, which you should write to the side of the issue just as there was previously.
- Continue doing this till the outcome is 0.

The resulting octal number is represented by the remainders you noted alongside the division difficulties. Since the least significant digit will be at the top and the most significant digit will be at the bottom, the number should be read from bottom to top.

## Hex to Octal Conversion Table

Hexadecimal Number | Octal Number |
---|---|

0 | 0 |

1 | 1 |

2 | 2 |

3 | 3 |

4 | 4 |

5 | 5 |

6 | 6 |

7 | 7 |

8 | 10 |

9 | 11 |

a | 12 |

b | 13 |

c | 14 |

d | 15 |

e | 16 |

f | 17 |

10 | 20 |