Base Conversion Method

Base Conversion of Whole Numbers

Base conversion of whole numbers is fairly easy if you use remainders.

Let's start with an example:

Convert 1208 to base-26

(base 26 is fun because it is the Alphabet)

Watch this series of divisions (R means remainder, which is ignored in the next division):

Now, think about the last answer (1 R 20), it means that 1208/26/26 = 1 (plus bits), in other words it tells us that we should put a "1" in the "26²" column!!!

Next we should put a 20 in the "26¹" column, and lastly a 12 in the units.

Why?

Becasue our division work just before has really said that:

1208 = 46 × 26 + 12

So, 12 belongs in the units column, and from here on we are dealing with the first power of 26:

46 = 1 × 26 + 20 (so 20 belongs in the ×26 column, and we put 1 in the ×26×26 column)

And if we substitute letters for numbers we get: ATL

Now, let's see if it has worked:
1 × 26² = 676
+20 × 26 = 520
+12 × 1 = 12
==> Total: 1208

So, to do whole numbers you do repeated divisions and put the results in from right to left

Note: if you use the A=0 style, then the code ATL is really B__ (you figure it out!)

What happens after the Decimal Point?

Now, if you have followed how to do whole numbers, we can look at "decimals" (hmmm... not an accurate word becuase it implies base-10 but you know what I mean).

To do "decimals", you use repeated multiplies and build from left to right.

Let us try an example using PI (3.1416...), and convert it to base-26. The whole number part is easy, it converts into base-26 as 3, so next we move on to the "decimal" part:

.1416 × 26 = 3.6816
.6816 × 26 = 17.7216
.7216 × 26 = 18.7616
etc...

The first answer says to put a 3 in the first "decimals" column, the second answer says to put a 17 in the second column etc ..

So the answer is:

And if we substitute letters for numbers we get: C.CQR

As a check I calculated 3 + 3/26 + 17/26² + 18/26³ = 3.141556..., and that looks pretty good!