Binary Octal Conversion Calculator
Convert between binary and octal number systems with our powerful calculator tool
Enter only 0s and 1s
Conversion Results
Input Value
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Result
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Select "Show conversion steps" to see detailed calculation process.
📚 Number Systems Explained
Binary System (Base-2)
Uses only two digits: 0 and 1. Fundamental to all digital systems and computer operations.
Example: 10102 = 1010
Octal System (Base-8)
Uses digits from 0 to 7. Commonly used in computing as a more compact representation of binary.
Example: 128 = 1010
Decimal System (Base-10)
The standard system using digits 0-9. What humans use for everyday counting.
Example: 1010 = A16
📊 Binary-Octal-Decimal Conversion Table
| Binary | Octal | Decimal | Hex |
|---|---|---|---|
| 0000 | 0 | 0 | 0 |
| 0001 | 1 | 1 | 1 |
| 0010 | 2 | 2 | 2 |
| 0011 | 3 | 3 | 3 |
| 0100 | 4 | 4 | 4 |
| 0101 | 5 | 5 | 5 |
| 0110 | 6 | 6 | 6 |
| 0111 | 7 | 7 | 7 |
| 1000 | 10 | 8 | 8 |
| 1001 | 11 | 9 | 9 |
| 1010 | 12 | 10 | A |
Note: This table shows the fundamental relationships between number systems.
🔍 Common Binary-Octal Conversions
10102 = 128
Basic conversion example
11112 = 178
Nibble to octal
1000002 = 408
Power of two conversion
1010102 = 528
Pattern example
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Note: This calculator provides accurate conversions between number systems. For extremely large numbers, precision may be limited by JavaScript's number handling capabilities.