Convert byte array into any base

Question

I have an array of bytes (any length), and I want to encode this array into string using my own base encoder. In .NET is standard Base64 encoder, but what if I want to encode the array in Base62, Base53 or Base13?

Is it even possible to create such universal base encoder?

I know I could do it the simple way, that is, for each byte reserve fixed number of chars (in case of Base62, that would be 5 chars), and do direct byte->chars encoding, but I would be wasting space, as 5 Base62 chars are able to contain more than 1 byte, but less than 2 bytes.

How should I write such an encoder? Or is there already some class for this?
And please note that I need universal decoder as well, otherwise this is useless to me.

Resources

As the solution is already known (use BigInteger), I would just like to put here some resources relating the BigInteger class, as it is not available in .NET 3.5:

Big integers in C#
http://intx.codeplex.com/
https://svn.apache.org/repos/asf/incubator/heraldry/libraries/csharp/openid/trunk/Mono/Mono.Math/BigInteger.cs
http://www.codeproject.com/KB/cs/BigInteger_Library.aspx
http://www.codeproject.com/KB/cs/biginteger.aspx

Answer 1

Here is a copy from my blog which I hope helps how (and why) I convert to Base62

I am currently working on my own url shortener: konv.es. In order to create the shortest possible character hash of the url, I use the GetHashCode() method of the string, then convert the resulting number to base 62 ([0-9a-zA-Z]). The most elegant solution that I have found thus far to make the convertion (which is also a handy-dandy example of a yield return) is:

public static IEnumerable<char> ToBase62(int number)
    {
        do
        {
            yield return "0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ"[number % 62];
            number /= 62;

        } while (number > 0);
    }

Extra credit: re-factor as an extension method

Answer 2

I've written an article which describes a solution in Python that exactly deals with your problem. I didn't use very special features of Python in order to get a solution which can easily be implemented in other languages. You might have a look and find out if it fits your needs.