# Converting Numbers into Bijective Base-26

January 3, 2020

So recently I was working on a side project where I wanted to change a sequence of numbers to a sequence of characters: 0 = A, 1 = B … 25 = Z, 26 = AA. Similar to how Microsoft Excel and other spreadsheets number their column headers.

My first thought was its just a Base10 to Base26 conversion and then map the resulting values of each digit to their corresponding character.

Nope, that does not work. If you think about it, if A = 0 and B = 1 then 10 = BA and you get a sequence of A,B,C…Z, BA, BB, BC. That’s correct Base26 but its not what I wanted.

After some searching with google, I found out that the name of this kind of numbering system is called Bijective Base26 or Base 26 without a zero. Thanks Wikipedia!

After some further googling to find examples of an algorithm, I cobbled together a few chunks of pseudo code (props to yabob) to come up with the following ruby implementation:

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ALPHABET = %w(A B C D E F G H I J K L M N O P Q R S T U V W X Y Z) def alphabase(n, letters = []) len = ALPHABET.length if (n >= len) alphabase(n/len - 1, letters) n = n % len end letters << ALPHABET[n] letters.join end alphabase(0) => 'A' alphabase(25) => 'Z' alphabase(26) => 'AA' |

Maybe someone will find this useful. It’s also probably a fun interview question to ask a candidate