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Re: Bijective basechanger

Newsgroups comp.lang.javascript
Date 2014-06-17 14:07 -0700
References <e8847026-67f9-417c-9166-d1368bb9a704@googlegroups.com> <60b6a006-1e9e-4b16-8056-243992faedcb@googlegroups.com> <5da0343a-ede6-473a-ae01-58bf34739171@googlegroups.com> <56a7f5f9-25d0-4d19-a545-939eedfdb424@googlegroups.com>
Message-ID <9b0b48bb-020b-4b5d-bd1e-2033a0891d61@googlegroups.com> (permalink)
Subject Re: Bijective basechanger
From jonas.thornvall@gmail.com

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Den tisdagen den 17:e juni 2014 kl. 22:54:02 UTC+2 skrev Michael Haufe (TNO):
> On Tuesday, June 17, 2014 3:23:15 PM UTC-5, jonas.t...@gmail.com wrote:
> 
> 
> 
> > Ok base 16 but lets 10=A,B...,C...,D...,E...,F,*G*=16 so  253=F13 
> 
> > 
> 
> > Well using base 16 if we would use your suggeste method to convert 240 it would end up be F0?
> 
> > 
> 
> > But I want a zeroless encoding (bijective?) EG=(14*16)+(16*1)
> 
> 
> 
> If you're using juxtaposition to represent the tuple (which is ambiguous), then
> 
> yes, 240 as a base 16 encoding would be F0.
> 
> 
> 
> You seem to be using the term "bijective" in a strange way. The above encoding I
> 
> presented _is_ bijective.
> 
> 
> 
> I don't understand your requirement of a "zeroless encoding"
> 
> 
> 
> Another approach is to convert the integer into prime factors, but it will be
> 
> quite slow:
> 
> 
> 
> 864 = (2^5)*(3^3)
> 
> 
> 
> Also, there do exist positional number systems that don't use "0", but
> 
> honestly I think I want to know the context of your requirement better

I am not sure what to say about it is an zeroles encoding scheme for the natural numbers. Problem is i do not remember howto approach the problem i Think it must be pairwise from lowest to highest.


BASE 10
1=1
10=A 
20=1A          =10+10
30=2A          =20+10
30=3A          =30+10
100=9A         =90+10
101=A1         =100+1
200=19A        =100+90+10
201=1A1        =100+100+1
1000=99A       =900+90+10
2000=199A      =1000+900+90+10
2001=19A1      =1000+900+100+1
2010=19AA      =1000+900+100+10
2014=1A14      =1000+1000+14

And here you have ternary using same principle

BASE3
   Deroless             Ordinary
1 =1 	1		01 
2 =2 	2		02 
3 =3 	3		10 
4 =11 	3+1 		11 
5 =12 	3+2 		12 
6 =13 	3+3 		20 
7 =21 	6+1 		21 
8 =22 	6+2 		22 
9 =23 	6+3 		100 
10=31 	9+1 		101 
11=32 	9+2 		102 
12=33 	9+3 		110 
13=111	9+3+1 		111 
14=112 	9+3+2 		112 
15=113 	9+3+3 		120 
16=121 	9+6+1 		121 
17=122 	9+6+2 		122 
18=123 	9+6+3 		200 
19=131 	9+9+1 		201 
20=132 	9+9+2 		202 
21=133 	9+9+3 		210 
22=211 	18+3+1
23=212 	18+3+2
24=213 	18+3+3
25=221	18+6+1
26=222 	18+6+2
27=223 	18+6+3

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Thread

Bijective basechanger jonas.thornvall@gmail.com - 2014-06-17 06:42 -0700
  Re: Bijective basechanger "Michael Haufe (TNO)" <tno@thenewobjective.com> - 2014-06-17 12:08 -0700
    Re: Bijective basechanger jonas.thornvall@gmail.com - 2014-06-17 13:23 -0700
      Re: Bijective basechanger jonas.thornvall@gmail.com - 2014-06-17 13:24 -0700
      Re: Bijective basechanger "Michael Haufe (TNO)" <tno@thenewobjective.com> - 2014-06-17 13:54 -0700
        Re: Bijective basechanger jonas.thornvall@gmail.com - 2014-06-17 14:07 -0700
          Re: Bijective basechanger jonas.thornvall@gmail.com - 2014-06-17 14:15 -0700
            Re: Bijective basechanger John Harris <niam@jghnorth.org.uk.invalid> - 2014-06-23 17:23 +0100
        Re: Bijective basechanger jonas.thornvall@gmail.com - 2014-06-17 14:23 -0700
        Re: Bijective basechanger jonas.thornvall@gmail.com - 2014-06-17 14:41 -0700
          Re: Bijective basechanger "Michael Haufe (TNO)" <tno@thenewobjective.com> - 2014-06-17 20:28 -0700
            Re: Bijective basechanger jonas.thornvall@gmail.com - 2014-06-18 13:04 -0700
              Re: Bijective basechanger "Michael Haufe (TNO)" <tno@thenewobjective.com> - 2014-06-18 16:30 -0700
                Re: Bijective basechanger jonas.thornvall@gmail.com - 2014-06-18 17:45 -0700
                Re: Bijective basechanger jonas.thornvall@gmail.com - 2014-06-18 17:49 -0700
                Re: Bijective basechanger "Michael Haufe (TNO)" <tno@thenewobjective.com> - 2014-06-19 11:21 -0700
                Re: Bijective basechanger jonas.thornvall@gmail.com - 2014-06-19 14:44 -0700
                Re: Bijective basechanger jonas.thornvall@gmail.com - 2014-06-19 14:48 -0700
                Re: Bijective basechanger jonas.thornvall@gmail.com - 2014-06-19 14:55 -0700
                Re: Bijective basechanger "Michael Haufe (TNO)" <tno@thenewobjective.com> - 2014-06-19 19:59 -0700
                Re: Bijective basechanger jonas.thornvall@gmail.com - 2014-06-21 09:25 -0700
                Re: Bijective basechanger jonas.thornvall@gmail.com - 2014-06-21 11:15 -0700
                Re: Bijective basechanger jonas.thornvall@gmail.com - 2014-06-18 18:05 -0700
                Re: Bijective basechanger jonas.thornvall@gmail.com - 2014-06-18 18:19 -0700
                Re: Bijective basechanger jonas.thornvall@gmail.com - 2014-06-18 18:25 -0700
                Re: Bijective basechanger jonas.thornvall@gmail.com - 2014-06-18 18:46 -0700
            Re: Bijective basechanger "Michael Haufe (TNO)" <tno@thenewobjective.com> - 2014-06-23 16:00 -0700
              Re: Bijective basechanger "Michael Haufe (TNO)" <tno@thenewobjective.com> - 2014-06-23 17:51 -0700
  Re: Bijective basechanger John Harris <niam@jghnorth.org.uk.invalid> - 2014-06-23 17:18 +0100
    Re: Bijective basechanger jonas.thornvall@gmail.com - 2014-06-23 11:27 -0700
  Re: Bijective basechanger Scott Sauyet <scott.sauyet@gmail.com> - 2014-06-23 15:29 -0700
    Re: Bijective basechanger jonas.thornvall@gmail.com - 2014-06-24 03:26 -0700
      Re: Bijective basechanger jonas.thornvall@gmail.com - 2014-06-24 03:28 -0700
      Re: Bijective basechanger jonas.thornvall@gmail.com - 2014-06-24 04:24 -0700
        Re: Bijective basechanger jonas.thornvall@gmail.com - 2014-06-24 05:36 -0700
        Re: Bijective basechanger Scott Sauyet <scott.sauyet@gmail.com> - 2014-06-24 13:05 -0700
          Re: Bijective basechanger jonas.thornvall@gmail.com - 2014-06-24 14:13 -0700
            Re: Bijective basechanger jonas.thornvall@gmail.com - 2014-06-25 05:36 -0700
            Re: Bijective basechanger Scott Sauyet <scott.sauyet@gmail.com> - 2014-06-25 12:45 -0700
              Re: Bijective basechanger Scott Sauyet <scott.sauyet@gmail.com> - 2014-06-25 13:15 -0700
                Re: Bijective basechanger jonas.thornvall@gmail.com - 2014-07-01 02:39 -0700
                Re: Bijective basechanger Scott Sauyet <scott.sauyet@gmail.com> - 2014-07-03 07:33 -0700
                Re: Bijective basechanger jonas.thornvall@gmail.com - 2014-07-03 09:54 -0700
                Re: Bijective basechanger jonas.thornvall@gmail.com - 2014-07-04 02:14 -0700
                Re: Bijective basechanger Scott Sauyet <scott.sauyet@gmail.com> - 2014-07-05 12:12 -0700
                Re: Bijective basechanger "Evertjan." <exxjxw.hannivoort@inter.nl.net> - 2014-07-05 22:19 +0200
                Re: Bijective basechanger Scott Sauyet <scott.sauyet@gmail.com> - 2014-07-05 13:50 -0700
                Re: Bijective basechanger jonas.thornvall@gmail.com - 2014-07-06 11:11 -0700
                Re: Bijective basechanger jonas.thornvall@gmail.com - 2014-07-06 14:59 -0700
                Re: Bijective basechanger jonas.thornvall@gmail.com - 2014-07-06 15:00 -0700
                Re: Bijective basechanger jonas.thornvall@gmail.com - 2014-07-06 15:02 -0700
                Re: Bijective basechanger jonas.thornvall@gmail.com - 2014-07-16 23:31 -0700
                Re: Bijective basechanger jonas.thornvall@gmail.com - 2014-07-04 02:28 -0700
                Re: Bijective basechanger Scott Sauyet <scott.sauyet@gmail.com> - 2014-07-05 12:14 -0700
          Re: Bijective basechanger jonas.thornvall@gmail.com - 2014-06-25 22:38 -0700
    Re: Bijective basechanger jonas.thornvall@gmail.com - 2014-06-24 03:32 -0700
    Re: Bijective basechanger jonas.thornvall@gmail.com - 2014-06-24 03:44 -0700
    Re: Bijective basechanger jonas.thornvall@gmail.com - 2014-06-24 11:10 -0700
      Re: Bijective basechanger Scott Sauyet <scott.sauyet@gmail.com> - 2014-06-24 11:45 -0700
  Re: Bijective basechanger "Chris M. Thomasson" <no@spam.invalid> - 2014-07-22 12:16 -0700

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