title: Reason for end around carry to do
body: <p>I know that the r-1 complement for r-base number should do end around carry if the highest bit has carry.</p>
  
  <p>But I cannot figure out why it should do it.</p>
  
  <p>I merely can think about it is the reason may be about the two representations for zero.</p>
  
  <p>ex:</p>
  
  <pre><code> 1 1 1 0    (-1)
   0 1 0 1    (+5)  
   ===============
  10 0 1 1  =====&gt;(0 1 0 0)
  I just can explain it from the result that because its sum is positive, and 1's complement has two representations, so it should add one.
  </code></pre>
  
  <p>ex:</p>
  
  <pre><code> 1 1 1 0    (-1)
   1 0 1 0    (-5)  
   ===============
  11 0 1 1  =====&gt;(1 0 0 1)
  And I cannot explain it why should add one.
  </code></pre>
  
  <p>What is the really reason for end around carry?</p>
  
  <p>Thx for you reading it.</p>