title: Two's complement binary multiplication
body: <p>I'm confused about where I'm going wrong in the following problem using binary multiplication with two's complement.</p>
  
  <p>I am trying to multiply <code>12 * -6</code>.</p>
  
  <p>We know that <code>12 = 01100</code> and <code>-6 = 11010</code>, and sign-extended we get <code>00000 01100 * 11111 11010</code>.  I tried multiplying these two numbers as follows:</p>
  
  <pre><code>     1111111010
     x 0000001100
     ------------
       0000000000
      0000000000
     1111111010
  + 1111111010
  ---------------
   10111110111000
  </code></pre>
  
  <p>This is definitely not <code>-72</code>, so what am I doing wrong?</p>