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Re: IEEE-754-2008 2's complement question

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On Sunday, March 4, 2012 1:12:57 PM UTC, Daku wrote:
> Could some computer architecture guru please
> clarify this a bit ?
> Suppose I have a signed fraction as -0.25
> The IEEE-754-2008 representation(with
> "hidden bit") of it is:
> 
> Sign       Exponent       Mantissa
> 1            01111110       1.0000000000000000000000
> 
> Now suppose I wish to add it to 100.0
> First of all, the 2's complement of the
> mantissa has to be obtained. The
> question is whether the "hidden bit" is
> also inverted.
> 
> If yes, the 2's complement for this
> mantissa is
> 0.11111111111111111111111
>                                           1
> Resulting in, after the above addition
> in 1.000000000000000000000000
> 
> Is this reasoning correct ? Or is the
> "hidden bit" not taken into account
> in the 2's complement calculation ?

No.  Back around 1981 I wrote microcode to implement 
this floating-point representation on a bit-slice 
processor, so it goes (as far as I remember now):

(a) the exponent of your 100.0 is way way bigger 
than the exponent of 0.25, so to align the exponents:-

(b) logically shift the 0.25 fraction and its hidden 
bit 9 places to the right, and (notionally only) 
increment its exponent by 9.

(c) the exponents now match, so according to the 
signs of the fractions and the specified operation 
(+ or -), add or subtract them, including the hidden 
bit of the larger fraction.  When it's subtraction 
instead of addition, then of course the smaller 
fraction will be fully 2's complemented.

(d) in this case we will just re-hide the hidden 
bit of the result fraction, but ...

(e) in other subtraction cases we may have to 
shift the result fraction up 1 or more places, 
and in the case of addition we may have to shift 
the result fraction down 1 place, adjusting the 
exponent appropriately in either case.

That's it, apart from correct result rounding 
(can be quite a pain) and underflow and overflow.
-- 

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IEEE-754-2008 2's complement question Daku <dakupoto@gmail.com> - 2012-03-04 05:12 -0800
  Re: IEEE-754-2008 2's complement question Mark Thorson <nospam@sonic.net> - 2012-03-04 10:37 -0800
    Re: IEEE-754-2008 2's complement question BGB <cr88192@hotmail.com> - 2012-03-04 13:21 -0700
      Re: IEEE-754-2008 2's complement question BGB <cr88192@hotmail.com> - 2012-03-04 13:49 -0700
    Re: IEEE-754-2008 2's complement question Quadibloc <jsavard@ecn.ab.ca> - 2012-03-04 13:08 -0800
      Re: IEEE-754-2008 2's complement question BGB <cr88192@hotmail.com> - 2012-03-04 14:43 -0700
      Re: IEEE-754-2008 2's complement question Mark Thorson <nospam@sonic.net> - 2012-03-04 16:35 -0800
        Re: IEEE-754-2008 2's complement question John Levine <johnl@iecc.com> - 2012-03-05 01:39 +0000
          Re: IEEE-754-2008 2's complement question Mark Thorson <nospam@sonic.net> - 2012-03-04 18:53 -0800
            Re: IEEE-754-2008 2's complement question John Levine <johnl@iecc.com> - 2012-03-05 04:04 +0000
              Re: IEEE-754-2008 2's complement question Mark Thorson <nospam@sonic.net> - 2012-03-04 21:13 -0800
                Re: IEEE-754-2008 2's complement question Terje Mathisen <"terje.mathisen at tmsw.no"> - 2012-03-05 08:27 +0100
                Re: IEEE-754-2008 2's complement question BGB <cr88192@hotmail.com> - 2012-03-05 01:21 -0700
                Re: IEEE-754-2008 2's complement question Jean-Marc Bourguet <jm@bourguet.org> - 2012-03-08 16:57 +0100
                Re: IEEE-754-2008 2's complement question Terje Mathisen <"terje.mathisen at tmsw.no"> - 2012-03-08 18:55 +0100
                Re: IEEE-754-2008 2's complement question Stefan Monnier <monnier@iro.umontreal.ca> - 2012-03-05 17:01 -0500
        Re: IEEE-754-2008 2's complement question Joe Pfeiffer <pfeiffer@cs.nmsu.edu> - 2012-03-04 22:32 -0700
  Re: IEEE-754-2008 2's complement question MitchAlsup <MitchAlsup@aol.com> - 2012-03-04 11:46 -0800
  Re: IEEE-754-2008 2's complement question bert <bert.hutchings@btinternet.com> - 2012-03-04 12:05 -0800
    Re: IEEE-754-2008 2's complement question dakupoto@gmail.com - 2012-03-04 19:40 -0800
      Re: IEEE-754-2008 2's complement question Joe Pfeiffer <pfeiffer@cs.nmsu.edu> - 2012-03-04 22:33 -0700
      Re: IEEE-754-2008 2's complement question bert <bert.hutchings@btinternet.com> - 2012-03-05 02:16 -0800
  Re: IEEE-754-2008 2's complement question Quadibloc <jsavard@ecn.ab.ca> - 2012-03-04 13:09 -0800

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