Edit in JSFiddle

$(function() {
    var input = $('input');
    
    $('button#toDec').click(function() {
           	var val = input.val();
        	var decimal = hexavigesimal.toDecimal(val);
        	$('span').text(decimal);
           	return;
    });
    
        $('button#toHex').click(function() {
           	var val = input.val();
        	var alpha = hexavigesimal.toAlphaNumber(val);
        	$('span').text(alpha);
           	return;
    });


});

var hexavigesimal = function() {
  var _alphabet = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";

  var self = this;

  self.toDecimal = function(alphaNumber) {
    if (!alphaNumber.match(/[a-z]/i)) {
        alert('Input must be alphabetic')
        return;}
    var _alphaNumber = alphaNumber.toUpperCase();
    var decimalValues = _alphaNumber.split("").reverse().map(function(char, index) {
      return self.charToDecimal(char) * Math.pow(26, index);
    });

    return decimalValues.reduce(function(memo, num) {
      return memo + num;
    }, 0);
  };

  self.toAlphaNumber = function(decimal) {
    if (!decimal.match(/^\d+$/)) {
        alert('Input must be numeric');
        return;
  }
        
    var remainders = [], remainder = 0;

    for (var counter = 1; remainder != decimal; counter++) {
      remainder = decimal % (Math.pow(26, counter));
      remainders.push(remainder);
    }

    var mappedChars = remainders.map(function(remainder, index) {
      var charCode = Math.floor(remainder / (Math.pow(26, index)));

      return self.decimalToChar(charCode);
    });

    return mappedChars.reverse().join("");
  };

  self.charToDecimal = function(char) {
    return _alphabet.indexOf(char) + 1;
  };

  self.decimalToChar = function(decimal) {
    return _alphabet.substring(decimal - 1, decimal);
  };

  return self;
}();

<h2>Convert between decimal and hexavigesimal</h2>

<div>
    Input:
    <input id="decimal" type="text" />
</div>

<strong>Output:</strong>
<span id="output"></span>

<br>
    
<button id="toDec">To Decimal</button>
<button id="toHex">To Hexavigesimal</button>