Binary / Decimal / Hex Converter
Instantly convert numbers between binary (base 2), octal (base 8), decimal (base 10), and hexadecimal (base 16). This free converter is essential for programming, computer science, and digital electronics.
Number base conversion is a fundamental skill in computer science and digital electronics. Computers operate in binary (0s and 1s), but humans prefer decimal. Hexadecimal provides a compact representation of binary data.
Base Systems:
- Binary (base 2): Uses digits 0 and 1. Each digit is a bit. Eight bits make a byte. Example: 1010 in binary = 10 in decimal.
- Octal (base 8): Uses digits 0-7. Each octal digit represents exactly 3 binary digits. Used in Unix file permissions.
- Decimal (base 10): Our everyday number system using digits 0-9.
- Hexadecimal (base 16): Uses digits 0-9 and letters A-F. Each hex digit represents exactly 4 binary digits (a nibble). Widely used in programming for memory addresses, color codes (#FF5733), and byte values.
Conversion Methods:
To convert from any base to decimal, multiply each digit by its positional power of the base and sum the results. To convert from decimal to another base, repeatedly divide by the target base and collect remainders.