Float Question

Tim Olson tim at jumpnet.com
Thu Dec 31 14:07:00 UTC 1998

>>> 52 bits of significand.
>As I sit listening to Professor Kahan on tape while reading "52", I see
>on the other monitor the number 53.  The larger number is actually the
>right one, despite the fact that 53+11+1 > 64, because, for normal
>numbers, the leading bit of the significand is boring.  It is always on.
>That's what normalization does, after all.  Since it is so boring, we
>need not even store it.

Yes, you are right.  To be precise I should have said 52 bits of 
"fraction", not "significand", although you'll find that many texts also 
use these two words interchangeably, adding to the confusion.

Excerpt from the PowerPC Architecture Manual:
  Representation of numeric values in the floating-point formats
  consists of a sign bit (S), a biased exponent (EXP), and the fraction
  portion (FRACTION) of the significand.  The significand consists of a
  leading implied bit concatenated on the right with the FRACTION.  This
  leading implied bit is 1 for normalized numbers and 0 for denormalized
  numbers and is located in the unit bit position (i.e., the first bit
  to the left of the binary point).

     -- tim

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