Base Converter
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Decimal
Denary (Base 10)Binary
Radix 2 (Base 2)Hexadecimal
Hex (Base 16)Octal
Oct (Base 8)Custom Base (Base 3)
Supports Radix 2 to 360-2.Understanding Numeric Base Systems
In computing and mathematics, a base (or radix) is the number of unique digits, including zero, used to represent numbers in a positional numeral system. While humans traditionally use the decimal system (Base 10) due to having ten fingers, digital electronics rely exclusively on the binary system (Base 2) representing electrical on/off states (1 and 0).
Hexadecimal (Base 16)
Hexadecimal is widely used in computer science because it can represent 4 binary bits (one nibble) as a single character. It utilizes digits 0-9 and lettersA-F (representing 10-15). For example, hex FF equals decimal 255.
Octal (Base 8)
Octal numbers use digits 0-7. Historically popular for PDP-11 systems and UNIX file permissions, where each octal digit represents exactly 3 bits. For example, permission 755 corresponds to binary111 101 101.
Fractional Conversions
Converting fractional values (digits after the decimal dot) involves multiplying the fractional remainder by the target base, extracting the integer part as the next digit, and repeating the process on the remaining fraction. Some base-10 fractions (like 0.1) become infinite recurring fractions in base-2 (0.000110011...).