why was this classified??<p>in any case this is really clever.  the norm-squared of 1+i in the Gaussian integers is (1+i)(1-i) = 1 + 1 = 2.  the norm is sqrt(2).<p>another way to think of this is we can color a checkerboard like this:<p><pre><code>  xoxoxoxo
  oxoxoxox
  xoxoxoxo
  oxoxoxox
</code></pre>
The o&#x27;s are &quot;even&quot; in this binary system and the x&#x27;s are &quot;odd&quot;<p>So in a sense this is the &quot;square-root&quot; of the binary numbers in the complex intgers Z[i]<p>I wonder then how &quot;carries&quot; work in this binary system?