Base Converter Tool

This online live tool lets you convert between bases in arbitrary precision. Decimal, binary, hex, octal - any base up to 36. It arbitrary precision which means you can enter values of any length and immediately see the results. The base in the third row is configurable so if you want to convert to vigesimal (base-20) enter 20 in to this field. Values between 2 and 36 are supported.

Base Systems

The main base systems in use in computing today are decimal (base 10), hexadecimal (base 16) and binary (base 2). Octal (base 8) is common these days. A number in a given base or radix is represented by digits in positional notation. That is, each digit in a number has a value which comes from its position and the value assigned to the digit itself. The values 1 to 9 are obviously represented by the digits '1' to '9' however for bases over 10 letters are used to represent highter values. For example the value 10 is represented by 'A', 11 by 'B' and so on. The positional value assigned to each digit depends on its position from the right in the number. In hex (base 16) the right most character has a positional value of 1 (160), the next 16 (161), the next 256 (162), and so on.

To convert a number in another base to decimal it is just a matter of multipling the positional value of each digit with its digit value and adding the results. For example B4F in hex is equal to 11*256 + 4*16 + 15*1 = 2895 (where B=1 and F=15).

A more detailed treatment of this subject can be found on Wikipedia