🎓 Mathematics • Mathematical Conversions
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Octal Converter
Converts base-8 numbers to decimal, binary, hex, and translates 3-digit octals into Unix chmod permissions.
🎱 Octal (Base-8) Universal Converter
Convert octal numbers into Decimal, Binary, Hexadecimal, and decode Unix file permissions (chmod).
Only octal digits (0, 1, 2, 3, 4, 5, 6, 7) are accepted
Multi-Base Formats for 0o755
Octal (Base-8)0o755Plain: 755
CopyDecimal (Base-10)493Sum: 493
CopyBinary (Base-2)1111011013-bit Trios: 111 101 101
CopyHexadecimal (Base-16)0x1EDPlain: 1ED
CopyUnix Permissions (chmod)-rwxr-xr-xSymbolic notation
Copy🔒 Unix File Permissions (chmod 755) Breakdown
Owner (User)7
rwx
Read (4)Write (2)Exec (1)
Group5
r-x
Read (4)Write (2)Exec (1)
Others (World)5
r-x
Read (4)Write (2)Exec (1)
📐 Mathematical Place Value Expansion (Base-8 to Base-10)
| Position (i) | Digit (d_i) | Place Value (8^i) | Contribution (d_i × 8^i) |
|---|---|---|---|
| 8^2 | 7 | 64 | +448 |
| 8^1 | 5 | 8 | +40 |
| 8^0 | 5 | 1 | +5 |
| Total Decimal Value | 493 | ||
What is Octal?
The octal numeral system is base-8, using digits 0 through 7. Each octal digit corresponds to exactly 3 binary bits.
Formula & Step-by-Step Calculation
N = ∑ dᵢ × 8ⁱ
Positional powers of 8 summation.
Worked Step-by-Step Examples
Example 1
Convert 755 to Unix chmod
Solution: -rwxr-xr-x
• 7 = rwx, 5 = r-x, 5 = r-x
Common Real-World & Academic Use Cases
- ✓ Unix file permission chmod configuration
- ✓ Legacy computing architectures
- ✓ Aviation transponder squawk codes
How to Use the Octal Converter
1
Enter Octal
Input octal digits (0-7).
2
View Permissions
Inspect decimal, binary, and Unix permissions.
Frequently Asked Questions
Q: What is chmod 777?
Read, write, and execute permissions granted to owner, group, and public.