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copied!<p>First off, neither IEEE-754-2008 nor -1985 have 16-bit floats; but it is a proposed addition with a 5-bit exponent and 10-bit fraction. IEE-754 uses a dedicated sign bit, so the positive and negative range is the same. Also, the fraction has an implied 1 in front, so you get an extra bit.</p> <p>If you want accuracy to the ones place, as in you can represent each integer, the answer is fairly simple: The exponent shifts the decimal point to the right-end of the fraction. So, a 10-bit fraction gets you ±2<sup>11</sup>.</p> <p>If you want one bit after the decimal point, you give up one bit before it, so you have ±2<sup>10</sup>.</p> <p>Single-precision has a 23-bit fraction, so you'd have ±2<sup>24</sup> integers.</p> <p>How many bits of precision you need after the decimal point depends entirely on the calculations you're doing, and how many you're doing.</p> <ul> <li>2<sup>10</sup> = 1,024</li> <li>2<sup>11</sup> = 2,048</li> <li>2<sup>23</sup> = 8,388,608</li> <li>2<sup>24</sup> = 16,777,216</li> <li>2<sup>53</sup> = 9,007,199,254,740,992 (double-precision)</li> <li>2<sup>113</sup> = 10,384,593,717,069,655,257,060,992,658,440,192 (quad-precision)</li> </ul> <h2>See also</h2> <ul> <li><a href="https://en.wikipedia.org/wiki/Double_precision" rel="nofollow noreferrer" title="Double-precision on Wikipedia">Double-precision</a></li> <li><a href="https://en.wikipedia.org/wiki/Half_precision" rel="nofollow noreferrer" title="Half-precision on Wikipedia">Half-precision</a></li> </ul>

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