A way to convert a decimal number to an arbitrary base string representation and back

gistfile1.js

// Converts a given decimal number into a base 26 string representation, e.g.
//   0     -> A
//   1     -> B
//   25    -> Z
//   26    -> BA
//   26*26 -> BAA
function stringCodeFromNumber(number) {
  return stringifyNumberArray(convertDecimalToNewBase(number, 26, 0), "A");
}

// Converts a string to a decimal number. Takes as arguments the base
// of the number represented in the string, and the zeroth letter.
// E.g. numberFromStringCode("BAA", 26, "A") -> 676 (26 * 26)
function numberFromStringCode(string, base, zerothLetter) {
  var numberArray = numberArrayFromString(string, zerothLetter);
  var result = 0;
  for (var i = 0; i < numberArray.length; i++) {
    var power = numberArray.length - i - 1;
    result += numberArray[i] * Math.pow(base, power);
  }
  return result;
}

// Takes a decimal number and returns an array of numbers representing digits
// in the new base.
function convertDecimalToNewBase(number, newBase, power) {
  var nextPower = power + 1;
  var nextDivisor = Math.pow(newBase, nextPower);
  var remainder = number % nextDivisor;
  var divisor = Math.pow(newBase, power);
  var digit = remainder / divisor;
  var rest = number - remainder;

  if (rest === 0) {
    return [digit];
  }
  return convertDecimalToNewBase(rest, newBase, power + 1).concat([digit]);
}

// Takes a number array and returns a string by converting each digit
// in the array into a letter based on the given zeroth letter.
function stringifyNumberArray(numberArray, zerothLetter) {
  var result = '';
  var zerothLetterValue = zerothLetter.charCodeAt(0);
  for(var i = 0; i < numberArray.length; i++) {
    var number = numberArray[i];
    result += String.fromCharCode(zerothLetterValue + number);
  }
  return result;
}

// Converts a string into an array of digits, given the zeroth letter.
function numberArrayFromString(string, zerothLetter) {
  var numberArray = [];
  var zerothLetterValue = zerothLetter.charCodeAt(0);
  for(var i = 0; i < string.length; i++) {
    numberArray.push(string.charCodeAt(i) - zerothLetterValue);
  }
  return numberArray;
}

This is a lot more flexible than you need for your problem but it was bugging me.

It works by converting the given decimal number to a base 26 representation, then converting that to a string. Unfortunately, that doesn't really fit the scheme of A,B,C...Z, AA, AB, AC, ... ZZ, AAA because you can't use A to represent zero and one.