title: Multiply two Binary numbers as a String without using Integer
body: <p>so I've been struggeling about this task, where I have to write a java code to multiply 2 binary numbers as a String. I have no idea how to multiply these and save them in seperate Strings so I can add them at the end. May someone might give me some hints how I could start or something like that?
  I have to do the multiplication with the given Strings and cannot convert them into an Integer. I know how to do the multiplication on paper but have no ideo how to put that into code.
  That's my code so far.</p>
  
  <pre><code>public static String multiply(String binary1, String binary2) {
  
     String b1 = new StringBuilder(binary1).reverse().toString();
     String b2 = new StringBuilder(binary2).reverse().toString();
  
     int[] m = new int[binary1.length()+binary2.length()];
  
     for (int i = 0; i &lt; binary1.length(); i++) {
          for (int j = 0; j &lt; binary2.length(); j++) {
              m[i+j] += (b1.charAt(i)-'0')*(b2.charAt(j)-'0');
          }
     }
  
     StringBuilder sb = new StringBuilder();
  
     for(int i=0; i &lt; m.length; i++) {
        int mod = m[i]%10;
        int carry = m[i]/10;
        if (i+1 &lt; m.length) {
          m[i + 1] = m[i + 1] + carry;
        }
        sb.insert(0, mod);
     }
     // remove front zeros
     while (sb.charAt(0) == '0' &amp;&amp; sb.length() &gt; 1) {
          sb.deleteCharAt(0);
     }
     return sb.toString();
  }
  public static void main(String[] args) {
      Scanner scan = new Scanner(System.in);
      System.out.print("1. Factor:  ");
      String input1 = scan.next("(0|1)*");
      System.out.print("2. Factor:  ");
      String input2 = scan.next("(0|1)*");
      scan.close();
      System.out.println("Result: " + multiply(input1, input2));
  }
  </code></pre>