title: Float and double - Significand numbers- Mantissa POV?
body: <p>With <em>Single</em> precision (32 bits): the bits division goes <a href="http://www.dspguide.com/ch4/3.htm" rel="nofollow noreferrer"><em>like this</em></a> : </p>
  
  <p><img src="https://i.stack.imgur.com/6d0dD.jpg" alt="enter image description here"></p>
  
  <p>So we have <em>23</em> bits of mantissa/Significand . </p>
  
  <p>So we can represent 2^23 numbers (via 23 bits ) :  which is <code>8388608</code> --> which is 7 digit long.</p>
  
  <p><strong>BUT</strong></p>
  
  <p>I was reading that the mantissa is normalized (<em>the leading digit in the mantissa will always be a 1</em>)  - so the pattern is actually <code>1.mmm</code> and <strong>only</strong> the <code>mmm</code> is represented in the mantissa.</p>
  
  <p>for example : look here : </p>
  
  <p><img src="https://i.stack.imgur.com/r7ZSa.jpg" alt="enter image description here"></p>
  
  <p>0.75 is represented but it's actually 1.75</p>
  
  <p><strong>Question #1</strong></p>
  
  <p>So basically it adds 1 more precision digit....no ? </p>
  
  <p>If so then we have 8 Significand  !</p>
  
  <p>So <em>why</em> does msdn says : 7 ?</p>
  
  <p><img src="https://i.stack.imgur.com/Ry4nH.jpg" alt="enter image description here"></p>
  
  <p><strong>Question #2</strong></p>
  
  <p>In double there are 52 bits for mantissa. (0..51)</p>
  
  <p>If I add 1 for the normalized mantissa so its 2^53 possibilites which is : <code>9007199254740992</code> ( 16 digits)</p>
  
  <p>and MS does say : 15-16 :</p>
  
  <p><img src="https://i.stack.imgur.com/VF6de.jpg" alt="enter image description here"></p>
  
  <p>Why is this inconsistency ? am I missing something ? </p>