base number systems are everywhere; believe me.  we use our money in base 10, use time (in general) in base 60, 24, and 365, and computer memory is in base 16 and 2.  i know some of you know how to count binary on your hands, it's not that hard and it's in the h4ndb00k.  but how many of us actually know how to convert from one of these to the other?  there's basically two ways to do this.  first, convert from the base-n number to base-10 (decimal), then convert from base-10 to base-n.  and second, convert the first directly into the second.  i have yet to find out how to program that one though, although i know how to, it's complicated. i'll be showing you how to do the first.

NOTE: i will be refering to base-n as b-n for now on.  example: base-10 is b-10

There's a basic method to convert to b-10 from any other base. lets use b-2 (binary) as an example.

110101 (b-2) is 53 (b-10)

you can find that by taking the sum of each digit times the base to the (length-position) power.
with the base as n, the digit as d, the position as x, and the length as l: 

(summation: x=0 to l) d * n^(l-x)

using this with "110101" (b-2) you get:

(1 * 2^(6-1)) + (1 * 2^(6-2)) + (0 * 2^(6-3)) + (1 * 2^(6-4)) + (0 * 2^(6-5)) + (1 * 2^(6-6)) = 53

for all the math geeks out there, they will notice that if the digit is zero, they can ignore it (you get zero..) and the last one is always the digit's value itself. this formula works for every b-n to b-10 conversion.

to convert from b-10 to base-n, it's a bit more complicated.