Computers think in binary (base 2), humans count in decimal (base 10), and programmers often use hexadecimal (base 16) as a human-friendly shorthand for binary. This converter bridges all four common number bases simultaneously — change any one value and see the others update in real time, with bit-level visualization and step-by-step conversion math.
How to Use the Converter
Enter a number in any base and all others update live:
- Binary: Use only 0 and 1 (e.g., 11111111)
- Octal: Use digits 0-7 (e.g., 377)
- Decimal: Standard numbers (e.g., 255)
- Hex: Use 0-9 and A-F (e.g., FF)
Understanding Number Bases
Each base uses a different set of digits and positional values:
- Binary (base 2): Each position is a power of 2: 1, 2, 4, 8, 16, 32...
- Octal (base 8): Groups of 3 binary digits: 011 = 3, 111 = 7
- Decimal (base 10): Each position is a power of 10: 1, 10, 100, 1000...
- Hex (base 16): Groups of 4 binary digits (nibbles): 1111 = F, 10100101 = A5
Where Each Base Is Used
- Binary: Hardware logic, network masks, file permissions (chmod)
- Octal: Unix file permissions (chmod 755), some legacy systems
- Decimal: Everyday math, user interfaces, financial calculations
- Hex: Color codes (#FF0000), memory addresses, MAC addresses, UUIDs
Step-by-Step Instructions
- 1Enter a number in any base field (binary, octal, decimal, or hex).
- 2All other fields update instantly with the converted values.
- 3View the bit-level visualization showing individual bits grouped in nibbles.
- 4Study the step-by-step conversion breakdown for educational purposes.
- 5Toggle between unsigned and signed integer interpretation.