Floating point limits
IEEE 754 - high bit sign bit, 8 bit biased exponent, 23 bit signficand.


Maximum absolute number size - 32 binary IEEE representation.
  0 1111 1110 1111 1111 1111 1111 1111 111

  Remember all 1s in exponent is special flag

Exponent
  8 bit biased exponent   2^(8-1)-1 = 127 bias

  1111 1110  = 254
           b  

  254 - 127 = 127   2^127

Signficand
  1111 1111 1111 1111 1111 111 = 23 bit mantissa

  1.1111 1111 1111 1111 1111 111 = with significant bit. 


  In decimal, it can be shown that 9 = 10^1 - 10^0


  The same can be done in binary :

  1.1111 1111 1111 1111 1111 111 (significand with hidden bit restored)
    can be restated as 

    10 - 0.0000 0000 0000 0000 0000 001  or 2^1 - 2^-23
      b                                b

Maximum absolute size is (2^1 - 2^-23)* 2^127  or  2^128 - 2^104
Minimum normalized number size
  32 binary representation.

  0 0000 0001 0000 0000 0000 0000 0000 000

  Remember all 0s in exponent is special flag

  Exponent
    8 bit biased exponent   2^(8-1)-1 = 127 bias

    0000 0001 = 1

    1 - 127 = -126   2^-126

  Signficand
    23 bit 0000 0000 0000 0000 0000 000

    (with implied bit in integer location)
    1.0000 0000 0000 0000 0000 000 * 2^-126 

  Minimum normalized size is 2^-126
Minimum denormalized number size
  32 binary representation.

  0 0000 0000 0000 0000 0000 0000 0000 001

  All 0s in exponent and a non-zero signficand flag a denormalized value.

  Exponent
    Assume the normalized smallest exponent. 1 - 127 = -126   2^-126

    0.0000 0000 0000 0000 0000 001

    1.0000 0000 0000 0000 0000 000 =1 * 2^-23

  Minimum normalized size is 1 * 2^-23 * 1 * 2^-126 = 1 * 2^-149