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Sep 22nd, 2014
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  1. Maximum absolute number size - 32 binary IEEE representation.
  2. 0 1111 1110 1111 1111 1111 1111 1111 111
  3.  
  4. Remember all 1s in exponent is special flag
  5.  
  6. Exponent
  7. 8 bit biased exponent 2^(8-1)-1 = 127 bias
  8.  
  9. 1111 1110 = 254
  10. b
  11.  
  12. 254 - 127 = 127 2^127
  13.  
  14. Signficand
  15. 1111 1111 1111 1111 1111 111 = 23 bit mantissa
  16.  
  17. 1.1111 1111 1111 1111 1111 111 = with significant bit.
  18.  
  19. If in decimal, it can be shown that 9 = 10^1 - 10^0
  20.  
  21. Then
  22. The binary above is 10 - 0.0000 0000 0000 0000 0000 001 or 2^1 - 2^-23
  23. b b
  24.  
  25. Maximum absolute size is (2^1 - 2^-23)* 2^127 or 2^128 - 2^104
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