Hexadecimal to Octal Converter
Enter the hexadecimal number you want to convert to octal.
Table of Contents
- How does hexadecimal to octal conversion work?
- Hexadecimal to octal conversion formula
- Conversion process
- Examples
- Hexadecimal to octal conversion table
- Frequently Asked Questions
How does hexadecimal to octal conversion work?
The hexadecimal system is base 16 and the octal system is base 8. To convert a hexadecimal number to octal, first convert each hexadecimal digit into its 4-bit binary equivalent. Then, group the bits in sets of three (from right to left) to obtain the number in base 8.
Hexadecimal to octal conversion formula
For a hexadecimal number with n digits:
N₁₆ = ∑(hi × 16i) → N₁₀ → N₈Each hexadecimal digit hi is first converted into a 4-bit binary group. Then, the complete binary number is grouped into sets of 3 bits (from right to left) to obtain its equivalent in base 8.
Conversion process
- Write the hexadecimal number.
- Convert each hexadecimal digit into its 4-bit binary equivalent (use A=1010, B=1011, C=1100, D=1101, E=1110, F=1111).
- Group all bits into sets of 3, starting from the right.
- Convert each 3-bit group into its corresponding octal value (000–111 → 0–7).
- Join all the obtained values to form the final octal number.
Examples
1A₁₆ to octal| Hexadecimal | Binary (4 bits) | Grouping (3 bits) | Octal |
|---|---|---|---|
| 1 | 0001 | 000 110 010 | 32 |
| A | 1010 |
Result: 1A₁₆ = 32₈.
2F₁₆ to octal| Hexadecimal | Binary (4 bits) | Grouping (3 bits) | Octal |
|---|---|---|---|
| 2 | 0010 | 000 101 111 | 137 |
| F | 1111 |
Result: 2F₁₆ = 137₈.
Hexadecimal to octal conversion table
Quick reference values for simple conversions between hexadecimal and octal.
| Hexadecimal | Octal |
|---|---|
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 |
1F | 37 |
FF | 377 |
Frequently Asked Questions
How do you convert a hexadecimal number to octal?
To convert a hexadecimal number to octal, first convert each hexadecimal digit into its 4-bit binary equivalent. Then, group the bits into sets of three (from right to left) and convert those groups into their corresponding octal values.
Why is the binary system used when converting from hexadecimal to octal?
The binary system serves as an intermediate step because both hexadecimal and octal are directly related to powers of 2. Each hexadecimal digit equals 4 bits, and each octal digit equals 3 bits. This makes the conversion from hexadecimal → binary → octal precise and straightforward, without needing to use the decimal system.