XOR function for two Hex byte arrays

I am trying to perform the exclusive or of two byte arrays and return the result as a hex string. I have converted the two byte array to their corresponding binary string. Each byte will have bits since it has 8 bytes.

byte[] key =  { 0x11, 0x12, 0x13, 0x14, 0x15, 0x16, 0x17, 0x18 };
byte[] PAN =  { 0x12, 0x22, 0x22, 0x22, 0x22, 0x22, 0x22, 0x23 };

Until now I have used a method that transforms the byte array into their corresponding binary string value, e.g. "10101010101". However when I perform the below method to get the XOR I am being returned with a string of bunch of smiley face which probably is some special ASCII character.

However I don't have any ideas how I can do this. I was thinking to convert the binary string to an integer, but that is not a good solution since it will not fit as an integer.

Do you have any ideas, please? possibly with some sample code?

public static string exclusiveOR(string string_1, string string_2)
{
        StringBuilder sb = new StringBuilder();
        for (int i = 0; i < string_1.Length; i++)
        sb.Append((char)(string_1[i] ^ string_2[(i % string_2.Length)]));
        String result = sb.ToString();

        return result;
}