title: Custom stream manipulator for streaming integers in any base
body: <p>I can make an <code>std::ostream</code> object output integer numbers in hex, for example</p>
  <pre><code>std::cout &lt;&lt; std::hex &lt;&lt; 0xabc; //prints `abc`, not the base-10 representation
  </code></pre>
  <p>Is there any manipulator that is universal for all bases? Something like</p>
  <pre><code>std::cout &lt;&lt; std::base(4) &lt;&lt; 20; //I want this to output 110
  </code></pre>
  <p>If there is one, then I have no further question.
  If there isn't one, then can I write one? Won't it require me to access private implementation details of <code>std::ostream</code>?</p>
  <p>Note that I know I can write a function that takes a number and converts it to a string which is the representation of that number in any base. Or I can use one that already exists. I am asking about custom stream manipulators - are they possible?</p>