IEEE 754 standard
  wikipedia topic :  IEEE 754 


feature
sign
exponent
significand
bits
1
8
23


Special conditions not representable by scientific or float notation.


Zero value.
 sign           significand
      exponent
  0   00000000  all-zeros (single precision - 23 digits)

  Both exponent and significand set to zero, sign bit may be either.


Infinity value.  
 sign  exponent  significand
  0    11111111  all-zeros 

  Exponent all 1s and significand set to zero


NAN - not a number.  
 sign  exponent  significand
  0    11111111  non-zero 

  Exponent all 1s and significand not zero

  Significand treated as a set of flags. (Wikipedia topic : NaN)
    A signaling NaN, sNaN, signals a condition that may further processed
      by special functions or float extensions.
      Once processed, may be converted to quiet NaNs.

    Quiet NaNs, qNaNs, usually represent an invalid operation.
      If possible, quiet NaNs are propagated through the computations so 
        they are properly identified in the solution.
  
    Most significan bit of significand may be used to note signal or quiet.
      Rest of the significand bits may provide a payload, which
        may be used.
    
  NAN is usually handled in software.


Denormalized.
 sign  exponent  significand
  0    00000000  non-zero (single precision)

  Exponent zero and significand not zero. 

  Allows for smaller magnitude values by sacrificing precision.
  Possible intermediate condition when doing decimal alignment 
    for calculations.

  
  Given a scientific decimal number with 4 decimal precision 
    and a 2 digit exponent.

    Smallest 'normal' value   1.0000 x 10^-99
   
      But, if we denormalize (fudge the rules).

    Smallest value   0.0001 x 10^-99

      No longer in normal scientific notation and we've lost most of 
        our precision, but magnitude or overall accuracy maintained.
    
    
  Note that software denormalization is very slow and can even present
    security risks. Some software will force denormalized values to zero.


Rounding.

  IEEE 754 lists 5 rounding protocols
   
  To nearest even

  To nearest, away from zero.

  Toward 0, (truncating)

  Toward +infinity

  Toward -infinity

  * Impossible to tell from already stored data unless source known.

  * Different math libraries may use different rounding.