Try this jsfiddle.

The more interesting functions to you are here. Not necessarily the cleanest or most efficient ones, but yea:

// converts binary string to a hexadecimal string
// returns an object with key 'valid' to a boolean value, indicating
// if the string is a valid binary string.
// If 'valid' is true, the converted hex string can be obtained by
// the 'result' key of the returned object
function binaryToHex(s) {
    var i, k, part, accum, ret = '';
    for (i = s.length-1; i >= 3; i -= 4) {
        // extract out in substrings of 4 and convert to hex
        part = s.substr(i+1-4, 4);
        accum = 0;
        for (k = 0; k < 4; k += 1) {
            if (part[k] !== '0' && part[k] !== '1') {
                // invalid character
                return { valid: false };
            }
            // compute the length 4 substring
            accum = accum * 2 + parseInt(part[k], 10);
        }
        if (accum >= 10) {
            // 'A' to 'F'
            ret = String.fromCharCode(accum - 10 + 'A'.charCodeAt(0)) + ret;
        } else {
            // '0' to '9'
            ret = String(accum) + ret;
        }
    }
    // remaining characters, i = 0, 1, or 2
    if (i >= 0) {
        accum = 0;
        // convert from front
        for (k = 0; k <= i; k += 1) {
            if (s[k] !== '0' && s[k] !== '1') {
                return { valid: false };
            }
            accum = accum * 2 + parseInt(s[k], 10);
        }
        // 3 bits, value cannot exceed 2^3 - 1 = 7, just convert
        ret = String(accum) + ret;
    }
    return { valid: true, result: ret };
}

// converts hexadecimal string to a binary string
// returns an object with key 'valid' to a boolean value, indicating
// if the string is a valid hexadecimal string.
// If 'valid' is true, the converted binary string can be obtained by
// the 'result' key of the returned object
function hexToBinary(s) {
    var i, k, part, ret = '';
    // lookup table for easier conversion. '0' characters are padded for '1' to '7'
    var lookupTable = {
        '0': '0000', '1': '0001', '2': '0010', '3': '0011', '4': '0100',
        '5': '0101', '6': '0110', '7': '0111', '8': '1000', '9': '1001',
        'a': '1010', 'b': '1011', 'c': '1100', 'd': '1101',
        'e': '1110', 'f': '1111',
        'A': '1010', 'B': '1011', 'C': '1100', 'D': '1101',
        'E': '1110', 'F': '1111'
    };
    for (i = 0; i < s.length; i += 1) {
        if (lookupTable.hasOwnProperty(s[i])) {
            ret += lookupTable[s[i]];
        } else {
            return { valid: false };
        }
    }
    return { valid: true, result: ret };
}

You're writing a string value into your Buffer object rather than a numerical value that it expects. Replace the line:

var hex = parseInt(value1, 2).toString(16); 

with:

var hex = parseInt(value1, 2); 

"a8" is really just the integer value 168 (you'll find if you console.log(value1) before your var hex = parseInt(value1, 2).toString(16); line, you'll get 10101000 (168 in binary)). When you write this value to the buffer, you really just want to write the integer value, not the string "a8".

The "hex value" as you put it, is actually just a number, hex is simply a presentation format. You don't store "hex numbers" or "binary numbers", you just store the numbers themselves.

As a result doing this you'll find console.log(hex); outputs 168 instead and think "That's wrong though!", but it's not, because 168 is a8.

The reason why you'll find it works with some values but not others is because any values which result in a purely numerical hex value (e.g. "22" or "67") will be automatically converted the their numerical equivalent (22 or 67). In your case however "a8" the value cannot be converted to the number type required by the buffer and so is discarded and 0 is written.

'b' is correct. Hexadecimal doesn't specify letter case, and many write hex strings with lower-case letters.

You can create a function converting a hex number to binary with something like this :

function hex2bin(hex){
    return ("00000000" + (parseInt(hex, 16)).toString(2)).substr(-8);
}

For formatting you just fill a string with 8 0, and you concatenate your number. Then, for converting, what you do is basicaly getting a string or number, use the parseInt function with the input number value and its base (base 16 for hex here), then you print it to base 2 with the toString function. And finally, you extract the last 8 characters to get your formatted string.

2018 Edit :

As this answer is still being read, I wanted to provide another syntax for the function's body, using the ES8 (ECMAScript 2017) String.padStart() method :

function hex2bin(hex){
    return (parseInt(hex, 16).toString(2)).padStart(8, '0');
}

Using padStart will fill the string until its lengths matches the first parameter, and the second parameter is the filler character (blank space by default).

End of edit

To use this on a full string like yours, use a simple forEach :

var result = ""
"21 23 00 6A D0 0F 69 4C E1 20".split(" ").forEach(str => {
  result += hex2bin(str)
})
console.log(result)

The output will be :

00100001001000110000000001101010110100000000111101101001010011001110000100100000

Using built-in functions:

parseInt('1010101010', 2).toString(16)

parseInt("10101001", 2).toString(16)
// => "a9"

EDIT: I think I misunderstood the question. Your data starts out as Buffer, then you convert it to a string, then you want it as hex? If so, just do data.toString('hex'). If you have already manipulated bindata, then reconstruct into a buffer:

var bindata = data.toString('binary');
// do something with bindata
var hexdata = new Buffer(bindata, 'ascii').toString('hex');

Here's something you can copy-paste in.

byteArray = new Uint8Array([181,143,16,173,231,56,63,149,181,185,224,124,84,230,123,36]);
function toHexString(byteArray) {
  return Array.prototype.map.call(byteArray, function(byte) {
    return ('0' + (byte & 0xFF).toString(16)).slice(-2);
  }).join('');
}
function toByteArray(hexString) {
  var result = [];
  for (var i = 0; i < hexString.length; i += 2) {
    result.push(parseInt(hexString.substr(i, 2), 16));
  }
  return result;
}
hexString = toHexString(byteArray);
byteArray = toByteArray(hexString);

From here/here.

It looks like you bytes were encoded as latin1:

let data = "53656e742066726f6d20796f7572205477696c696f20747269616c206163636f756e74202d20bf43f36d6f20657374e1733f"
let b = Buffer.from(data, 'hex')
console.log(b.toString('latin1'))

Prints

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