Octal to Hexadecimal Conversion Calculator
Use this calculator to convert octal (base 8) numbers into hexadecimal (base 16). Useful for developers, students, and digital engineers.
Understanding Octal to Hexadecimal Conversion
What is the Octal Number System?
The octal (base-8) number system uses eight digits: 0 through 7. Each position in an octal number represents a power of 8. This system was historically used in early computing, especially in systems where binary was too long and hexadecimal was not yet standardized.
What is the Hexadecimal System?
Hexadecimal (base-16) uses sixteen distinct symbols: 0–9 and A–F. Each digit represents four binary bits, making it compact and efficient for representing large binary values in programming, memory addressing, and digital logic.
Why Convert Octal to Hexadecimal?
Conversion between octal and hexadecimal is common in computer science and electronics. Although both serve as human-readable representations of binary, hexadecimal is more commonly used in modern computing. Converting between these formats allows interoperability between legacy systems and modern code.
How to Convert Octal to Hexadecimal
The conversion from octal to hexadecimal is typically done in two steps:
- Step 1: Convert octal to binary. Each octal digit maps to 3 binary bits.
- Step 2: Group the resulting binary digits into 4-bit segments (from right to left) and convert each segment into a hexadecimal digit.
Example: Convert Octal 1750 to Hex
- Octal 1 → 001
- 7 → 111
- 5 → 101
- 0 → 000
Binary: 001111101000
Group into 4 bits from right: 0011 1110 1000
- 0011 → 3
- 1110 → E
- 1000 → 8
Final Hex: 3E8
Result: Octal 1750 = Hexadecimal 3E8
Practical Examples
| Octal | Hexadecimal |
|---|---|
| 10 | 8 |
| 100 | 40 |
| 377 | FF |
| 1750 | 3E8 |
| 7777 | FFF |
Frequently Asked Questions
Can I enter letters or symbols in the octal input?
No. Octal numbers only use digits from 0 to 7. Letters or invalid digits like 8 or 9 will be rejected.
How large can my octal number be?
You can enter large octal numbers. The converter will handle them correctly up to browser memory and performance limitations.
Is this conversion exact?
Yes, it uses binary as an intermediate step, so the result is accurate and lossless.
Why is hexadecimal preferred over octal today?
Hexadecimal is more compact and aligns perfectly with byte boundaries (8 bits = 2 hex digits). It's also more common in modern programming languages and tools.
How are octal and hex stored internally?
Both are stored as binary inside a computer. Octal and hexadecimal are just human-friendly representations of the binary data.