Number Base Converter
Convert between Binary (base 2), Octal (base 8), Decimal (base 10), and Hexadecimal (base 16). Type in any field and all others update instantly.
Number Systems Reference
- Binary (base 2): Digits 0–1. Used internally by all computers.
- Octal (base 8): Digits 0–7. Used in Unix file permissions, some legacy systems.
- Decimal (base 10): Digits 0–9. The everyday number system.
- Hexadecimal (base 16): Digits 0–9, A–F. Used for colors, memory addresses, byte values.
Quick Reference Table
| Decimal | Binary | Octal | Hex |
|---|---|---|---|
| 0 | 0000 | 0 | 0 |
| 1 | 0001 | 1 | 1 |
| 4 | 0100 | 4 | 4 |
| 8 | 1000 | 10 | 8 |
| 10 | 1010 | 12 | A |
| 15 | 1111 | 17 | F |
| 16 | 10000 | 20 | 10 |
| 255 | 11111111 | 377 | FF |
Frequently Asked Questions
What is binary (base 2)?
Binary is a base-2 number system using only digits 0 and 1. It is the native language of computers — every piece of data is ultimately stored as binary. For example, the decimal number 10 is 1010 in binary.
What is hexadecimal (base 16)?
Hexadecimal (hex) uses 16 symbols: 0–9 and A–F. It is widely used in computing because one hex digit represents exactly 4 binary bits — making it a compact, human-readable way to express binary values. Colors in CSS (#ff6600), memory addresses, and byte values are commonly expressed in hex.
What is octal (base 8)?
Octal uses digits 0–7. It was common in older computing systems and is still used in Unix/Linux file permissions (e.g., chmod 755 means rwxr-xr-x). One octal digit represents exactly 3 binary bits.
How do I convert binary to decimal?
Multiply each binary digit by 2 raised to its position (right to left, starting at 0), then sum the results. For example, 1010 = (1×8) + (0×4) + (1×2) + (0×1) = 10. Our converter does this instantly for any input.
What does 0x prefix mean?
The 0x prefix indicates a hexadecimal number in most programming languages (C, Java, JavaScript, Python). Similarly, 0b indicates binary and 0o indicates octal. Example: 0xFF = 255 in decimal.