For two's complement to work, you need the leading bit to be 0 for
non-negative numbers.
Limiting the range of considered numbers (as you would for a fixed
width bit sequence) is one tool you can use here.
This can also be looked at as a padding issue (and the rude treatment
#:'s results get from frame fill can be motivating, for treating this
issue properly).
--
Raul
On Wed, Dec 14, 2011 at 11:02 AM, Devon McCormick <devon...@gmail.com> wrote:
> The "embarassing" example happens because the full scope of "two's
> complement" notation implies fixed-width binary numbers, not the
> variable-width version given in this thread.
>
> On Wed, Dec 14, 2011 at 10:41 AM, Kip Murray <k...@math.uh.edu> wrote:
>
>> On 12/14/2011 6:07 AM, Linda Alvord wrote:
>> > I really don't think that you can ever write a program good enough that
>> the
>> > the number 8 in binary is _8 in decimals
>> >
>> > hcinv 1 0 0 0
>> > _8
>>
>> THAT /IS/ EMBARRASSING !
>>
>> > I have lived my mathematical life without being able to write negative
>> > binary numbers. I have always ignored two's complements as beyond my
>> scope
>> > of interest. It is like saying there are no negative numbers. It will
>> be
>> > ok if 13 stands for _13 and we'll all be happy.
>> >
>> > I'm sure that much of the world deals well without imaginary numbers.
>> > However, they must have been a mess to develop so they work flawlessly.
>> > Note that they do have a strange appearance but if you understand them
>> you
>> > get used to them.
>> >
>> > In my world, if I want _8 I write _1 0 0 0 which is in the 8 4 2
>> 1
>> > 8's digit. So what is _14 ?
>> >
>> > Linda
>>
>> IN YOUR WORLD _14 IS
>>
>> - 1 1 1 0
>> _1 _1 _1 0
>>
>> AND IN TWO'S-COMPLEMENT IT IS
>>
>> tcng 0 1 1 1 0
>> 1 0 0 1 0
>>
>> ------------------
>>
>> stack =: ,.&.|: NB. stack x over y
>>
>> hv =: (0 {:: <"1) :: ] NB. return head vector
>>
>> Tbln =: 2 2 2 $ 0 0,1 1,1 1,0 1 NB. table for tcng, see opn
>>
>> ban =: 0 ,~ 0 ,.~ 0 ,.~ ] NB. build argument, see tcng
>>
>> opn =: ] stack~ (0 { [) , Tbln {~ [: < (0 { [) ,~ 2 { [: hv ]
>>
>> tcng =: (1 {"1 [: }: [: opn/ ban)"1 NB. TWO'S-COMPLEMENT NEGATIVE
>>
>> ----------------------------------------------------------------------
>> For information about J forums see http://www.jsoftware.com/forums.htm
>>
>
>
>
> --
> Devon McCormick, CFA
> ^me^ at acm.
> org is my
> preferred e-mail
> ----------------------------------------------------------------------
> For information about J forums see http://www.jsoftware.com/forums.htm
----------------------------------------------------------------------
For information about J forums see http://www.jsoftware.com/forums.htm
