Working with bases greater than 10. Just for fun.

Question

I'm trying to figure out how to work with math in higher than base 10. As an experiment, I started using base 26, using a = 0, b = 1, c = 2, and so on until z = 25. I then tried to calculate the value of my name, which is mark. The value I got was 18,317, but I have no idea how to check to see if I was right. Is there someone that can help me figure out what I'm doing or possibly an easier way to do it?

Answer 1

The usual way to represent bases greater than ten is to use 0 - 9 then A, B, C, etc. for 10, 11, 12, and so on. The hexadecimal (base 16) system, for instance is:

0 1 2 3 4 5 6 7 8 9 A B C D E F

Your system is a bit unconventional in that sense, but since it's just for fun I guess it's OK. Numbers have place value in any number system. For instance, the number 3724 in base 10 is:

3·10³ + 7·10² + 2·10¹ + 4·10⁰ = 3000 + 700 + 20 + 4 = 3724

For a 4 letter number (such as your name) in your base 26 system:

m·26³ + a·26² + r·26¹ + k·26⁰ = 12·26³ + 0·26² + 17·26¹ + 10·26⁰ = 211,364