Base Number Converter

A number base (or radix) determines how many unique digits are used to represent numbers. Decimal (base 10) uses digits 0-9, binary (base 2) uses 0-1, octal (base 8) uses 0-7, and hexadecimal (base 16) uses 0-9 and A-F. Each position in a number represents a power of the base, similar to how in decimal, 123 means 1×100 + 2×10 + 3×1.

Hexadecimal is popular in programming because each hex digit represents exactly 4 binary bits (a nibble). This makes it compact and easy to convert to binary mentally. For example, 0xFF in hex is 11111111 in binary—much shorter to write! It's commonly used for memory addresses, color codes (#FF0000), and byte values.

Octal (base 8) is most commonly used in Unix/Linux file permissions. Each digit represents 3 bits, perfect for the read (4), write (2), and execute (1) permission flags. For example, chmod 755 sets read+write+execute for owner, and read+execute for group and others.

The auto-detection feature checks for common prefixes first: 0b for binary, 0o for octal, and 0x for hexadecimal. If no prefix is found, it looks at the characters used. If the number contains A-F, it's assumed to be hex. If it only contains 0s and 1s and is longer than 4 digits, it's likely binary. Otherwise, it defaults to decimal.

Yes, but with limitations. Negative numbers can be entered in decimal format (e.g., -42). However, binary, octal, and hexadecimal representations of negative numbers require two's complement notation, which depends on the bit width (8-bit, 16-bit, 32-bit, etc.). This tool shows negative decimal values but indicates that other bases would need two's complement representation.

Yes, completely safe. This converter runs entirely in your browser using JavaScript. No data is ever sent to any server, stored, or logged. You can verify this by disconnecting from the internet—the tool will continue to work perfectly.