Base64String

How does one represent values in base-64 strings? Actually, the question is, what is the process of converting numerals from other bases to base 64 -- without using any library functions in any programming environment like .NET's Convert.ToString(byte[], int base) or Convert.ToBase64String? How does one do it on paper?

Going by the name, and the sparse documentation, I guess it is a system of representing numeral values where the logarithmic base is the number 64.

I pondered, like the binary system is base 2, it has two value representations -- 0 and 1. The decimal, base 10, has 10 value representations - 0 to 9. These we know of as digits of that system. In the base 64 system, the value representations, or digits, would then be 0 to 63. Wait a minute! But anything 10 or upward is already two digits. OK, that is so because I am representing them in base 10. So, the question is: what is that sample set of tokens which form the digits of base 64?

http://en.wikipedia.org/wiki/Base64