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Julia Evans (b0rk@social.jvns.ca)'s status on Saturday, 11-Feb-2023 02:17:47 JST Julia Evans

floating point representation
In conversation Saturday, 11-Feb-2023 02:17:47 JST from social.jvns.ca permalink
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1. 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
  https://cdn.masto.host/socialjvnsca/media_attachments/files/109/841/543/718/147/188/original/50ef83b5011afb0f.png
- Adrian Cochrane repeated this.
- Julia Evans (b0rk@social.jvns.ca)'s status on Saturday, 11-Feb-2023 04:02:01 JST Julia Evans
  in reply to
  
  Also https://float.exposed by Bartosz Ciechanowski is a great interactive website for poking at floating point numbers
  In conversation Saturday, 11-Feb-2023 04:02:01 JST permalink
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  1. No result found on File_thumbnail lookup.
    
    Float Exposed
    
    from Bartosz Ciechanowski
    
    Floating point format explorer – binary representations of common floating point formats.

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