• Public

  • Public
  • Network
  • Groups
  • Popular
  • People

subtitle: the 64-bit number line Floating point numbers aren't evenly distributed. Instead, between each power of 2 (from 2^-1023 to 2^1023), there are 2^52 numbers, evenly spaced. There 2^52 numbers between 2 and 4, between 4 and 8, -1/2 and -1/4, 1/16/ and 1/8, etc. floating point numbers are represented with 3 integers: 1. sign (+ or -, 0 is + and 1 is -) 2. exponent (the power of 2 3. significand (how far it is between that power of 2 and the next one) here's how to calculate the exponent and significand for 8.5: 1. find the powers of 2 that sound 8.5 (8 and 16) 2. calculate the exponent: 8 = 2^3, so the exponent is 3 3. calculate the significand: - 8.5 is 1/16 of the way between 8 and 16 - rewrite 1/16 as a fraction of 2^52, so 2^48 / 2^52 - So the significand is 2^48