/usr/share/doc/axiom-doc/hypertex/numrepeatingbinaryexpansions.xhtml

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  <div align="center"><img align="middle" src="doctitle.png"/></div>
  <hr/>
  <div align="center">Repeating Binary Expansions</div>
  <hr/>
All rational numbers have repeating binary expansions. Operations to 
access the individual bits of a binary expansion can be obtained by
converting the value to 
<a href="db.xhtml?RadixExpansion">RadixExpansion(2)</a>. More examples
of expansions are available in
<a href="numrepeatingdecimals.xhtml">DecimalExpansion</a>,
<a href="numrepeatinghexexpansions.xhtml">HexadecimalExpansion</a>, and
<a href="db.xhtml?RadixExpansion">RadixExpansion</a>. 

The expansion (of type 
<a href="db.xhtml?BinaryExpansion">BinaryExpansion</a>)
of a rational number is returned by the 
<a href="dbopbinary.xhtml">binary</a> operation.
<ul>
 <li>
  <input type="submit" id="p1" class="subbut" onclick="makeRequest('p1');"
    value="r:=binary(22/7)" />
  <div id="ansp1"><div></div></div>
 </li>
</ul>
Arithmetic is exact.
<ul>
 <li>
  <input type="submit" id="p2" class="subbut" 
    onclick="handleFree(['p1','p2']);"
    value="r+binary(6/7)" />
  <div id="ansp2"><div></div></div>
 </li>
</ul>
The period of the expansion can be short or long...
<ul>
 <li>
  <input type="submit" id="p3" class="subbut" onclick="makeRequest('p3');"
    value="[binary(1/i) for i in 102..106]" />
  <div id="ansp3"><div></div></div>
 </li>
</ul>
or very long
<ul>
 <li>
  <input type="submit" id="p4" class="subbut" onclick="makeRequest('p4');"
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  <div id="ansp4"><div></div></div>
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</ul>
These numbers are bona fide algebraic objects.
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 <li>
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    value="g:=gcd(p,q)" />
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axiom-hypertex-data 20120501-8 / usr / share / doc / axiom-doc / hypertex / numrepeatingbinaryexpansions.xhtml
