### Converting base n to base m

Hello guys, I was wondering if there is a standard for converting something like this:

HELLO 27 to ?3

If someone knows how, please explain. Thanks!
This is in Java, but you can still get the basic logic from it:
https://gist.github.com/LB--/4591371
(It doesn't do decimal places yet)

It's annoying to explain in words.
Thanks for that L B, but I was actually looking for a manual method of converting it. I sort of understand how it is done by machine code, but how would one convert that using pencil and paper?
OK.

Base 10 is the Decimal system, which we use. Take the number 123.45610 - it can also be written as:
100 + 20 + 3 + .4 + .05 + .006
This is called 'expanded form' and is taught to kids before 1st grade in elementary school.

The reason it is called base 10 is because there are 10 digits, 0-9. You can rewrite the expanded form as powers of 10:
1*102 + 2*101 + 3*100 + 4*10-1 + 5*10-2 + 6*10-3
This is how all numbers are represented. Similarly, Binary is base 2, because it has 2 digits, 0 to 1.

You can quite easily convert from base n to base m by taking advantage of dividing and taking the remainder. Let's look at 10010 and convert it to binary, for example:
 ```100 / 2 = 50, 100 % 2 = 0 50 / 2 = 25, 50 % 2 = 0 25 / 2 = 12, 25 % 2 = 1 12 / 2 = 6, 12 % 2 = 0 6 / 2 = 3, 6 % 2 = 0 3 / 2 = 1, 3 % 2 = 1 1 / 2 = 0, 1 % 2 = 1```
Result: 11001002

This process works for any base to any other base, so long as you know how to divide and take remainder of the base you're working with.

There is a convention for the digits above 9 in bases above 10. This is all the digits in base 62:
0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz
0-9, A-Z, a-z
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Here is what I did:

Convert to base 10 by getting the base 10 equivalent of the letters. So HELLO27 = 17 14 21 21 2410? I don't know if it is possible to do that so correct me if I'm wrong.

Then using the numbers in base 10, I convert to base 3 using your method and I got: 122 112 210 210 2203. Is this right?