[prev] 65 [next]

Floating Point Numbers (cont)

Example of normalising the fraction part in binary:
  • 1010.1011  is normalized as  1.0101011×2011
  • 1010.1011 = 10 + 11/16 = 10.6875
  • 1.0101011×2011 = (1 + 43/128) * 23 = 1.3359375 * 8 = 10.6875
The normalised fraction part always has 1 before the decimal point.

Example of determining the exponent in binary:

  • assume an 8-bit exponent, then bias B = 28-1-1 = 127
  • valid bit patterns for exponent  00000001 .. 11111110  (1..254)
  • exponent values   -126 .. 127