Kata from: http://www.codewars.com/kata/526a569ca578d7e6e300034e

Base Conversion

Description:

In this kata you have to implement a base converter, which converts between 
arbitrary bases / alphabets. Here are some pre-defined alphabets:

var Alphabet = {
  BINARY:        '01',
  OCTAL:         '01234567',
  DECIMAL:       '0123456789',
  HEXA_DECIMAL:  '0123456789abcdef',
  ALPHA_LOWER:   'abcdefghijklmnopqrstuvwxyz',
  ALPHA_UPPER:   'ABCDEFGHIJKLMNOPQRSTUVWXYZ',
  ALPHA:         'abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ',
  ALPHA_NUMERIC: '0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ'
};

The function convert() should take an input (string), the source alphabet (string) 
and the target alphabet (string). You can assume that the input value always 
consists of characters from the source alphabet. You don't need to validate it.

Examples:

// convert between numeral systems
convert("15", Alphabet.DECIMAL, Alphabet.BINARY); // should return "1111"
convert("15", Alphabet.DECIMAL, Alphabet.OCTAL); // should return "17"
convert("1010", Alphabet.BINARY, Alphabet.DECIMAL); // should return "10"
convert("1010", Alphabet.BINARY, Alphabet.HEXA_DECIMAL); // should return "a"

// other bases
convert("0", Alphabet.DECIMAL, Alphabet.ALPHA); // should return "a"
convert("27", Alphabet.DECIMAL, Alphabet.ALPHA_LOWER); // should return "bb"
convert("hello", Alphabet.ALPHA_LOWER, Alphabet.HEXA_DECIMAL); // should return "320048"
convert("SAME", Alphabet.ALPHA_UPPER, Alphabet.ALPHA_UPPER); // should return "SAME"
Additional Notes:

The maximum input value can always be encoded in a number without loss of precision
The function must work for any arbitrary alphabets, not only the pre-defined ones
You don't have to consider negative numbers

baseconvert.js

/* 
 *  I was practicing Recursion, Object methods, and functional programming. 
 *  Not an ideal solution is found, but meh...
 */
 
function convert(input, source, target) {
  
  // I convert everything to Base10 and then to all other
  function Converter(valueStr, source){
    this.src = {value: valueStr,
                   alphabet: source,
                   base: source.length}
    this.decimal = this.toBase10();
  }
  
  Converter.prototype.toBase10 = function(){
    var srcValueArray = this.src.value.split("");
    var srcAlphabet = this.src.alphabet;
    var base = this.src.base;    
    
    function alphabetToDecimal(char){
      return srcAlphabet.indexOf(char);
    }
    
    function reduceDecimal(array,result){
        var result = result || 0;            
        result += Math.pow(base,array.length-1) * array.shift();
        if(array.length === 0)
          return result;
        else
          return reduceDecimal(array,result);        
    }
  	
    return reduceDecimal(srcValueArray.map(alphabetToDecimal));
  }
  
   Converter.prototype.toBase = function(base,num,result){
    var result = result || [];
    var num = num || this.decimal;
    result.unshift(num % base);
    if (num < base)
      return result;
  	else
      return this.toBase(base,parseInt(num / base),result);
   }
  
  Converter.prototype.toAlphabet = function(alphabet){
    var alphabetBaseIntArray = this.toBase(alphabet.length);
    
    function charMapper(el){
      return alphabet.charAt(el);
    }
    
    return alphabetBaseIntArray.map(charMapper).join("");
  }
  
  
  // Start
  //============================
  //============================
  
  var number = new Converter(input, source);
  
  return number.toAlphabet(target);
  
}