[Math Lair] Base Conversion

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Converting a number from a base other than base 10 to base 10 is fairly simple. All that is required is to remember that the number is written in positional notation. For example, 463 in base 7 is simply 3 + 6 × 7 + 4 × 7 × 7, or 241 in base 10.

Converting a number from base 10 to another base is slightly more involved, but isn't complicated. It is an iterative process. To find the ones' digit, divide the number by the base. The ones' digit is the remainder. Repeat the process with the quotient to get the next place, and repeat while the quotient is greater than zero.

A similar process can be used to convert from an arbitrary base to another, but often it's just easier to convert the number from the original base to base 10, and then to the new base, simply because it's easier for us to think in base 10.

The following form converts numbers from one base to another.

Number to convert:
From base...
To base...

Note: For bases larger than 10, use the letters A–Z to represent digits with values 10–35 (i.e. A = 10, B = 11, ..., Z = 35).

I had originally written this in Java, but I've found that it didn't work well with certain browsers, so I've re-written it in Javascript. To view the Javascript source, simply view the source for this page. You can still view the (original) Java source code for the baseConvertor class and the displayNumber class.

View a list of other interactive content on this site.