An Algorithm for Converting Bases

Date: 2/2/96 at 16:19:14
From: Paul Frieden
Subject: base conversion

I would like a formula for base conversions.  My math teacher 
said that he had one, but now he can't find it.  Thank you.
Paul Frieden

Date: 2/6/96 at 14:52:18
From: Doctor Ethan
Subject: Re: base conversion

Hello Paul,

Here it is, butI wouldn't call it a formula. It is more like an algorithm.  
That means it is a method that always works, kind of like long division.

Here we go.

Let's say you have a number

10121 in base 3 

and you want to know what it is in base 10.  Well, in base three the 
place values are 

1,3,9,27,81

so we have 1 *81 + 0 * 27 + 1 * 9 + 2* 3 + 1* 1

81 +0+ 9 +6 +1 = 97

that is how it works.  You just take the number, figure out the place 
values, and then add them together to get the answer.  Now, let's do one 
the other way.

45 in base ten (that is the normal one.) Let's convert it to base five.

Well, in base five the place values will be 1,5,25,125

We won't have any 125's but we will have one 25. Then we will have 
20 left.  That is four 5's, so in base five our number will be 140.

Hope that makes sense.  If you don't see a formula, try to work 
out a bunch more examples and they should get easier.

-Doctor Ethan,  The Math Forum