Let me try again. I keep simplifying what I'm trying to explain. So here it is again. Maybe this will make some sense of what I'm saying:
]a=:8+i.15 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 ]b=:15#15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 ]c=:a-b _7 _6 _5 _4 _3 _2 _1 0 1 2 3 4 5 6 7 f=: 13 :'(x#2)#:y' f ] #:~ 2 #~ [ The function f converts the lists to binary numbers. The largest number 22 is less than 32 so only 5 digits are require. ]aa=:5 f a 0 1 0 0 0 0 1 0 0 1 0 1 0 1 0 0 1 0 1 1 0 1 1 0 0 0 1 1 0 1 0 1 1 1 0 0 1 1 1 1 1 0 0 0 0 1 0 0 0 1 1 0 0 1 0 1 0 0 1 1 1 0 1 0 0 1 0 1 0 1 1 0 1 1 0 ]bb=:5 f b 0 1 1 1 1 0 1 1 1 1 0 1 1 1 1 0 1 1 1 1 0 1 1 1 1 0 1 1 1 1 0 1 1 1 1 0 1 1 1 1 0 1 1 1 1 0 1 1 1 1 0 1 1 1 1 0 1 1 1 1 0 1 1 1 1 0 1 1 1 1 0 1 1 1 1 The result below is the difference in J between the two arrays above. It is not a conversion using #: ]cc=:aa-bb 0 0 _1 _1 _1 0 0 _1 _1 0 0 0 _1 0 _1 0 0 _1 0 0 0 0 0 _1 _1 0 0 0 _1 0 0 0 0 0 _1 0 0 0 0 0 1 _1 _1 _1 _1 1 _1 _1 _1 0 1 _1 _1 0 _1 1 _1 _1 0 0 1 _1 0 _1 _1 1 _1 0 _1 0 1 _1 0 0 _1 For comparison, the result cc2 is obtained as a J result using #: ]cc2=: 5 f c 1 1 0 0 1 1 1 0 1 0 1 1 0 1 1 1 1 1 0 0 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 1 1 0 0 1 0 0 0 0 1 0 1 0 0 1 1 0 0 0 1 1 1 Or: ]cc3=:#:c 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 Both cc2 and cc3 seem implausible because all numbers are known positive numbers. Now look at cc : w=: 13 :'(x,y)$|.2^i.y' w , $ [: |. 2 ^ [: i. ] 15 w 5 16 8 4 2 1 16 8 4 2 1 16 8 4 2 1 16 8 4 2 1 16 8 4 2 1 16 8 4 2 1 16 8 4 2 1 16 8 4 2 1 16 8 4 2 1 16 8 4 2 1 16 8 4 2 1 16 8 4 2 1 16 8 4 2 1 16 8 4 2 1 16 8 4 2 1 cc*15 w 5 0 0 _4 _2 _1 0 0 _4 _2 0 0 0 _4 0 _1 0 0 _4 0 0 0 0 0 _2 _1 0 0 0 _2 0 0 0 0 0 _1 0 0 0 0 0 16 _8 _4 _2 _1 16 _8 _4 _2 0 16 _8 _4 0 _1 16 _8 _4 0 0 16 _8 0 _2 _1 16 _8 0 _2 0 16 _8 0 0 _1 +/"1 cc*15 w 5 _7 _6 _5 _4 _3 _2 _1 0 1 2 3 4 5 6 7 This is c! Not only that, J knows it is c. #.cc _7 _6 _5 _4 _3 _2 _1 0 1 2 3 4 5 6 7 So what do you think? Linda -----Original Message----- From: programming-boun...@jsoftware.com [mailto:programming-boun...@jsoftware.com] On Behalf Of Devon McCormick Sent: Wednesday, December 14, 2011 5:04 PM To: Programming forum Subject: Re: [Jprogramming] How #: should have been designed So "8" would have to be represented by "0 1 0 0 0". On Wed, Dec 14, 2011 at 12:11 PM, Raul Miller <rauldmil...@gmail.com> wrote: > 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 > -- 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
