title: Why does the bit-width of the mantissa of a floating point represent twice as many numbers compared to an int?
body: <p>I am told that a <code>double</code> in C++ has a mantissa that is capable of safely and accurately representing [-(2<sup>53</sup> − 1), 2<sup>53</sup> − 1] integers.</p>
  <p>How is this possible when the mantissa is only 52 bits? Why is it that an <code>int16</code> is only capable of having a range of [-32,768, +32,767], or [-2<sup>15</sup>, 2<sup>15</sup>-1], when the same thing could be used for <code>int16</code> to allow twice as many representable numbers?</p>