How to convert Hexadecimal to Octal
Hexadecimal numbering system is one of the numeral systems that are commonly used in computers and other digital systems. It is base 16 and it has 16 symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 and A, B, C, D, E, F.
The octal numeral system is a numbering system that is based on 8 digits: 0, 1, 2, 3, 4, 5, 6, 7. It used to be popular in the early days of computing when it was primarily used for counting inputs and outputs, one byte at a time.
Table #1: Hexadecimal to Octal conversion table
| Hexadecimal | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | C | D | E | F |
| Octal | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 |
As with octal to hexadecimal, the easiest way to convert hexadecimal back to octal numbers is through binary conversion.
- Start with any hexadecimal number,
- Translate it into binary system by swapping each hexadecimal digit with the equivalent group of four binary digits,
- Drop any leading zeros from the resulting binary number, or pad it with zeros in order to achieve groups of three digits,
- Convert binary representation of the hexadecimal number into resulting octal number.
Table #2: Hexadecimal to Binary conversion table
| Hexadecimal | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | C | D | E | F |
| Binary | 0000 | 0001 | 0010 | 0011 | 0100 | 0101 | 0110 | 0111 | 1000 | 1001 | 1010 | 1011 | 1100 | 1101 | 1110 | 1111 |
Table #3: Binary to Octal conversion table
| Binary | 000 | 001 | 010 | 011 | 100 | 101 | 110 | 111 |
| Octal | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
Example #1: Convert hexadecimal 6F into octal
| Step description | Result |
|---|---|
| Translate 6F into binary | 0110 1111 |
| Pad one leading zero in order to achieve groups of 3 binary digits | 001 101 111 |
| Resulting octal number | 157 |
Example #2: Convert hexadecimal A16 into octal
| Step description | Result |
|---|---|
| Translate A16 into binary | 1010 0001 0110 |
| Form groups of 3 binary digits | 101 000 010 110 |
| Resulting octal number | 5026 |