JavaScript: Need functions to convert a string containing binary to hex, then convert back to binary

Why not using Array.prototype.reduce?

var binstr = "00001000010001000101010100001110"

function bin2hex(b) {
    return b.match(/.{4}/g).reduce(function(acc, i) {
        return acc + parseInt(i, 2).toString(16);
    }, '')
}

function hex2bin(h) {
    return h.split('').reduce(function(acc, i) {
        return acc + ('000' + parseInt(i, 16).toString(2)).substr(-4, 4);
    }, '')
}

console.log(binstr);
> 00001000010001000101010100001110
console.log(bin2hex(binstr));
> 0844550e
console.log(hex2bin(bin2hex(binstr)));
> 00001000010001000101010100001110

Link to jsfiddle here.

Notes:

1. In bin2hex, if you want to convert also trailing chunks of less than 4 bits to hex, replace {4} with {1,4}. However, converting back the result to binary, will produce a string that differs from the original. For example, converting forth and back "111101" would produce "11110001".
2. In hex2bin, binary values are left-padded with zeroes so as to have 4 binary digits for every hex digit.

Well I found an algorithm here which helped explain how to do it. Also this page on Wikipedia helped confirming the 4-bit binary to hexadecimal mappings. I came up with the following code to do it. Other code snippets I found on the web didn't work at all. Let me know if you would make any improvements. You could probably even do a straight lookup table really using that info from Wikipedia which would be faster.

var tools = {
    /**
     * Converts binary code to hexadecimal string
     * @param {string} binaryString A string containing binary numbers e.g. '01001101'
     * @return {string} A string containing the hexadecimal numbers
     */
    convertBinaryToHexadecimal: function(binaryString)
    {
        var output = '';

        // For every 4 bits in the binary string
        for (var i=0; i < binaryString.length; i+=4)
        {
            // Grab a chunk of 4 bits
            var bytes = binaryString.substr(i, 4);

            // Convert to decimal then hexadecimal
            var decimal = parseInt(bytes, 2);
            var hex = decimal.toString(16);

            // Uppercase all the letters and append to output
            output += hex.toUpperCase();
        }

        return output;      
    },

    /**
     * Converts hexadecimal code to binary code
     * @param {string} A string containing single digit hexadecimal numbers
     * @return {string} A string containing binary numbers
     */
    convertHexadecimalToBinary: function(hexString)
    {
        var output = '';

        // For each hexadecimal character
        for (var i=0; i < hexString.length; i++)
        {
            // Convert to decimal
            var decimal = parseInt(hexString.charAt(i), 16);

            // Convert to binary and add 0s onto the left as necessary to make up to 4 bits
            var binary = this.leftPadding(decimal.toString(2), '0', 4);

            // Append to string         
            output += binary;
        }

        return output;
    },

    /**
     * Left pad a string with a certain character to a total number of characters
     * @param {string} inputString The string to be padded
     * @param {string} padCharacter The character that the string should be padded with
     * @param {string} totalCharacters The length of string that's required
     * @returns {string} A string with characters appended to the front of it
     */
    leftPadding: function(inputString, padCharacter, totalCharacters)
    {
        // If the string is already the right length, just return it
        if (!inputString || !padCharacter || inputString.length >= totalCharacters)
        {
            return inputString;
        }

        // Work out how many extra characters we need to add to the string
        var charsToAdd = (totalCharacters - inputString.length)/padCharacter.length;

        // Add padding onto the string
        for (var i = 0; i < charsToAdd; i++)
        {
            inputString = padCharacter + inputString;
        }

        return inputString;
    }
};

To convert bin to hex and reverse i use these functions:

function bintohex()
{    
     mybin = document.getElementById('bin').value;

     z = -1; number = 0;
     for(i = mybin.length; i > -1; i--) 
     {
         //Every 1 in binary string is converted to decimal and added to number
         if(mybin.charAt(i) == "1"){
             number += Math.pow(2, z);
         }
         z+=1;
     }
     // Return is converting decimal to hexadecimal
     document.getElementById('result').innerHTML = number.toString(16);
}

function hextobin()
{
     mybin = "";
     /// Converting to decimal value and geting ceil of decimal sqrt
     myhex = document.getElementById('hex').value;
     mydec = parseInt(myhex, 16);
     i = Math.ceil( Math.sqrt(mydec) );
     while(i >= 0)
     {
         if(Math.pow(2, i) <= mydec){
             mydec = mydec-Math.pow(2, i);
             mybin += "1";
         }else if(mybin != "")
             mybin = mybin + "0";
             i = i-1;
         }
         document.getElementById('result').innerHTML = mybin;
}

Input binary: <input type = "text" id = "bin">
<button onclick = "bintohex()">Convert to Hex</button><br />

Input Hecadecimal: <input type = "text" id = "hex">
<button onclick = "hextobin()">Convert to Bin</button><br />

Results: <div id = "result"></div>

Don't forget to check your answer.