🎓 Computer Science • Number Systems
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Octal Converter (Base 8 ⇄ Bin, Dec, Hex)
Converts base-8 octal values using 3-bit binary triplet groupings and decimal expansions.
Presets:
Interactive Register Bit-Strip (Click Bits to Toggle)
Decimal (Base 10)
255
Signed 8-bit: -1 | Signed 16-bit: 255
Binary (Base 2)
1111 1111
Prefix:
0b11111111Hexadecimal (Base 16)
0xFF
Nibbles: F F
Octal (Base 8) & ASCII
0o377
ASCII Char: Non-printable
Positional Weight Expansion (Base 2)
(1 × 2^7 = 128) + (1 × 2^6 = 64) + (1 × 2^5 = 32) + (1 × 2^4 = 16) + (1 × 2^3 = 8) + (1 × 2^2 = 4) + (1 × 2^1 = 2) + (1 × 2^0 = 1) = 255
What is the Octal System?
The octal numeral system is the base-8 number system, using digits 0 to 7. Each octal digit represents exactly three binary bits.
Formula & Step-by-Step Calculation
1 Octal Digit = 3 Binary Bits (e.g. 7₈ = 111₂)
Positional expansion in powers of 8.
Worked Step-by-Step Examples
Example 1
Convert octal 755 (Unix permissions) to binary
Solution: 111 101 101 (rwxr-xr-x)
• 7 ⟹ 111, 5 ⟹ 101, 5 ⟹ 101
Common Real-World & Academic Use Cases
- ✓ Unix and Linux file permission chmod strings (755, 644)
- ✓ Legacy PDP computer architecture emulation
- ✓ Aeronautical transponder squawk codes
How to Use the Octal Converter (Base 8 ⇄ Bin, Dec, Hex)
1
Input Octal Digits
Enter digits 0 to 7.
2
Inspect Base Values
Review binary and decimal translations.
Frequently Asked Questions
Q: Where is octal used today?
Primarily in Unix/Linux filesystem permissions (e.g. chmod 777) and character escape sequences in C programming.