title: max float represented in IEEE 754
body: <p>I am wondering if the max float represented in IEEE 754 is:</p>
  
  <p><code>(1.11111111111111111111111)_b*2^[(11111111)_b-127]</code></p>
  
  <p>Here <code>_b</code> means binary representation. But that value is <code>3.403201383*10^38</code>, which is different from <code>3.402823669*10^38</code>, which is <code>(1.0)_b*2^[(11111111)_b-127]</code> and given by for example <code>c++</code> <code>&lt;limits&gt;</code>. Isn't 
  <code>(1.11111111111111111111111)_b*2^[(11111111)_b-127]</code> representable and larger in the framework?</p>
  
  <p>Does anybody know why?</p>
  
  <p>Thank you.</p>