Hexadecimal to Octal Conversion Calculator
Use this tool to convert hexadecimal numbers (base 16) into octal (base 8). Great for students, programmers, and electronics engineers.
Understanding Hexadecimal to Octal Conversion
What is Hexadecimal?
Hexadecimal (base 16) is a number system that uses 16 symbols: 0–9 and A–F. It's widely used in computing because each hex digit represents exactly 4 binary bits. It provides a more readable and compact form of binary values, making it popular in programming, memory addressing, and color representation in web design.
What is Octal?
Octal (base 8) uses only the digits 0 through 7. It is another positional number system frequently used in digital systems. Each octal digit corresponds to 3 binary bits, making it useful for compact representations of binary in systems such as UNIX file permissions and older machine code.
Why Convert from Hex to Octal?
Although hexadecimal and octal are both used to simplify binary data, they serve different roles. Converting from hex to octal may be necessary when working with systems that prefer base 8 representation or when analyzing machine-level outputs from legacy devices. It’s also a common requirement in academic and examination settings.
How the Conversion Works
The conversion from hexadecimal to octal is performed in two main steps:
- Hex → Binary: Convert each hex digit into its 4-bit binary equivalent.
- Binary → Octal: Group binary digits into sets of 3 bits (starting from the right), then convert each group into a single octal digit.
Example:
Convert 1F3 (hex) to octal:
- 1 → 0001
- F → 1111
- 3 → 0011
Binary string: 000111110011
Group into 3-bit chunks from the right: 000 111 110 011
Convert to octal:
- 000 → 0
- 111 → 7
- 110 → 6
- 011 → 3
Result: 0763
Practical Examples
| Hexadecimal | Octal |
|---|---|
| 1A | 032 |
| 3F | 077 |
| 7E9 | 1751 |
| FF | 377 |
| ABC | 5274 |
Frequently Asked Questions
Can I input lowercase letters?
Yes. Both lowercase and uppercase hex digits (a–f or A–F) are supported and interpreted the same.
How long can my hexadecimal input be?
You can enter very large hexadecimal numbers. The calculator supports inputs up to 64-bit or more, depending on your device performance and browser.
What if my hex input starts with 0x?
This tool expects raw hexadecimal digits only. Please omit any prefix such as 0x.
What happens if I enter an invalid character?
Only hexadecimal characters (0–9, A–F) are allowed. Any other input will trigger an error message prompting for valid input.
Is the conversion exact?
Yes. The conversion uses exact binary equivalents and positional alignment. No approximation or rounding is involved.