Free Octal to Binary Converter – Convert Base-8 to Binary Online
Convert octal (base-8) numbers to binary instantly with digit-by-digit visualization. Each octal digit converts to exactly 3 binary bits. Perfect for Unix permissions and programming. 100% free.
What Is Octal to Binary Conversion?
Octal to binary conversion transforms base-8 numbers (using digits 0-7) into base-2 numbers (using only 0 and 1). Since 8 = 2³, each octal digit maps to exactly 3 binary digits.
The Simple Rule
One octal digit = Three binary bits
This direct mapping makes octal-to-binary conversion one of the easiest number system conversions.
How to Convert Octal to Binary
Step-by-Step Method
- Take each octal digit separately
- Convert to 3-bit binary using the reference table
- Concatenate all binary groups
Conversion Reference
| Octal | Binary | Octal | Binary |
|---|---|---|---|
| 0 | 000 | 4 | 100 |
| 1 | 001 | 5 | 101 |
| 2 | 010 | 6 | 110 |
| 3 | 011 | 7 | 111 |
Conversion Examples
Example 1: Convert 754₈ to Binary
| Digit | 7 | 5 | 4 |
|---|---|---|---|
| Binary | 111 | 101 | 100 |
Result: 111101100₂
Example 2: Convert 377₈ to Binary
| Digit | 3 | 7 | 7 |
|---|---|---|---|
| Binary | 011 | 111 | 111 |
Result: 11111111₂ (255 in decimal)
Example 3: Convert 755₈ to Binary
| Digit | 7 | 5 | 5 |
|---|---|---|---|
| Binary | 111 | 101 | 101 |
Result: 111101101₂ (chmod permission)
Unix File Permissions
Octal to binary is essential for understanding Unix/Linux permissions:
Permission Bits Explained
| Octal | Binary | Meaning |
|---|---|---|
| 7 | 111 | rwx (read+write+execute) |
| 6 | 110 | rw- (read+write) |
| 5 | 101 | r-x (read+execute) |
| 4 | 100 | r-- (read only) |
| 3 | 011 | -wx (write+execute) |
| 2 | 010 | -w- (write only) |
| 1 | 001 | --x (execute only) |
| 0 | 000 | --- (no permission) |
Common chmod Values
| Octal | Binary | Permission String |
|---|---|---|
| 755 | 111101101 | rwxr-xr-x |
| 644 | 110100100 | rw-r--r-- |
| 777 | 111111111 | rwxrwxrwx |
| 600 | 110000000 | rw------- |
| 400 | 100000000 | r-------- |
Why Octal Is Used
Historical Reasons
- Early computers used 12-bit, 24-bit, or 36-bit words
- These divide evenly by 3 (the bits per octal digit)
- PDP-8 and other systems used octal extensively
Modern Uses
- Unix permissions: Standard representation
- ASCII codes: Sometimes expressed in octal
- Legacy systems: Some documentation uses octal
Programming Implementations
JavaScript
const octal = '755';
const binary = parseInt(octal, 8).toString(2);
// Result: '111101101'
Python
octal = '755'
binary = bin(int(octal, 8))
# Result: '0b111101101'
Manual Method (Any Language)
map = {'0':'000', '1':'001', '2':'010', '3':'011',
'4':'100', '5':'101', '6':'110', '7':'111'}
result = ''.join(map[digit] for digit in octal_string)
Common Conversions Reference
| Octal | Binary | Decimal |
|---|---|---|
| 1 | 1 | 1 |
| 10 | 1000 | 8 |
| 77 | 111111 | 63 |
| 100 | 1000000 | 64 |
| 377 | 11111111 | 255 |
| 777 | 111111111 | 511 |
Frequently Asked Questions
Why does each octal digit equal 3 binary bits?
Because 2³ = 8. Three bits can represent values 0-7, which matches the octal digit range exactly.
What happens with leading zeros?
Leading zeros in octal (like 007) still convert to 3 bits each. You can optionally trim leading zeros from the final result.
Can I use this for large numbers?
Yes! Simply convert each digit independently. The method works for any size octal number.
How is this different from hex to binary?
Hex uses 4 bits per digit (since 16 = 2⁴), while octal uses 3 bits per digit (since 8 = 2³).
What are invalid octal digits?
8 and 9 are not valid in octal. Valid digits are only 0, 1, 2, 3, 4, 5, 6, 7.
Tips for Quick Conversion
- Memorize the 8 values - Only 8 mappings to learn
- Think in threes - Each digit always becomes 3 bits
- Practice with permissions - Unix permissions make great practice
- Trim leading zeros - Remove them for cleaner results
Enter an octal number above to see instant binary conversion with step-by-step visualization.