Free Hex to Octal Converter – Convert Hexadecimal to Base-8 Online
Convert hexadecimal (base-16) numbers to octal (base-8) instantly. See the conversion path through decimal and binary. Perfect for understanding Unix permissions. 100% free.
What Is Hex to Octal Conversion?
Hexadecimal to octal conversion transforms base-16 numbers (using 0-9 and A-F) into base-8 numbers (using digits 0-7). This conversion is useful when working with Unix permissions or legacy systems.
Why Convert Hex to Octal?
While hex is more common in modern computing, octal remains important for:
- Unix file permissions: chmod uses octal notation
- Legacy systems: Some older documentation uses octal
- Educational purposes: Understanding number systems
How to Convert Hex to Octal
Method 1: Through Decimal
- Convert hex to decimal
- Convert decimal to octal
Method 2: Through Binary
- Convert each hex digit to 4 bits
- Regroup bits into sets of 3
- Convert each 3-bit group to octal
Step-by-Step Examples
Example 1: Convert 1ED₁₆ to Octal
Through Decimal:
- 1ED₁₆ = 1×256 + 14×16 + 13×1 = 493₁₀
- 493 ÷ 8 = 61 remainder 5
- 61 ÷ 8 = 7 remainder 5
- 7 ÷ 8 = 0 remainder 7
Result: 755₈ (chmod permission)
Through Binary:
- 1 → 0001
- E → 1110
- D → 1101
- Binary: 000111101101
- Regroup: 111 101 101
- Result: 755₈
Example 2: Convert FF₁₆ to Octal
Calculation:
- FF₁₆ = 255₁₀
- 255 ÷ 8 = 31 remainder 7
- 31 ÷ 8 = 3 remainder 7
- 3 ÷ 8 = 0 remainder 3
Result: 377₈ (maximum byte value)
Common Hex to Octal Conversions
| Hex | Decimal | Octal | Use Case |
|---|---|---|---|
| F | 15 | 17 | Single digit max |
| 10 | 16 | 20 | Hex 16 |
| FF | 255 | 377 | Max byte |
| 100 | 256 | 400 | 256 decimal |
| 1ED | 493 | 755 | rwxr-xr-x |
| 1A4 | 420 | 644 | rw-r--r-- |
| 1FF | 511 | 777 | rwxrwxrwx |
| 180 | 384 | 600 | rw------- |
Unix Permissions Reference
Converting hex addresses to octal permissions:
| Hex | Octal | Permission | Description |
|---|---|---|---|
| 1C0 | 700 | rwx------ | Owner full access |
| 1ED | 755 | rwxr-xr-x | Executable file |
| 1A4 | 644 | rw-r--r-- | Regular file |
| 1FF | 777 | rwxrwxrwx | Full access all |
| 1B6 | 666 | rw-rw-rw- | All read/write |
Hex vs Octal: Key Differences
| Feature | Hexadecimal | Octal |
|---|---|---|
| Base | 16 | 8 |
| Digits | 0-9, A-F | 0-7 |
| Bits per digit | 4 | 3 |
| Modern use | Very common | Limited |
| Prefix | 0x | 0o or 0 |
Programming Examples
JavaScript
const hex = '1ED';
const decimal = parseInt(hex, 16);
const octal = decimal.toString(8);
// Result: '755'
Python
hex_value = '1ED'
octal = oct(int(hex_value, 16))
# Result: '0o755'
Bash
printf "%o\n" 0x1ED
# Output: 755
Understanding the Conversion
Why Hex Doesn't Map Directly to Octal
Hex uses 4 bits per digit, octal uses 3 bits. Since 4 and 3 don't divide evenly, there's no direct digit-to-digit mapping.
Example:
- Hex F = binary 1111 (4 bits)
- Must regroup for octal: 01 111 → 1 7 → 17₈
Binary as Intermediate
Binary provides the cleanest intermediate representation:
- Hex → Binary (4 bits each)
- Regroup binary (3 bits each)
- Binary groups → Octal
Frequently Asked Questions
What is the 0x prefix?
The 0x prefix indicates hexadecimal notation. This tool accepts input with or without it.
Why is octal still used?
Unix permissions were designed with octal in mind, where each digit represents owner/group/other permissions.
Can I convert large hex numbers?
Yes, but very large numbers may exceed JavaScript's safe integer limit. For typical use cases, this isn't an issue.
How do I verify my conversion?
Convert back: octal → decimal → hex should give the original value.
Quick Mental Math Tips
- FF → 377: Max byte, memorize this
- 100 → 400: Power of 16 to power of 8
- Permissions: chmod values are always 3 octal digits
Enter a hexadecimal number above to see instant octal conversion with step-by-step visualization.