Converting base n to base m

[Smac89]

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!

[LB]

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.

[Smac89]

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?

[LB]

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

[Smac89]

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?

[LB]

Completely wrong, reread my post.