xkcd

by **FourTael** » Wed Jan 05, 2011 8:10 pm UTC

So we have hex. We have binary. We have base 110. How could I make it more complex?

By changing the bases dependant on the digit.

The base will be (distance from decimal place + 1). So the ones place will count up in base 2, the tens place will be base 3, the hundreds will be base 4, etc.

Here's an example of the first ten posts:

1
10
11
20
21
100
101
110
111
120

etc.

I shall start:

1

by **LucasBrown** » Wed Jan 05, 2011 9:05 pm UTC

And I shall skip to 11, since you have so kindly put the first bundle up. To aid in this, let's put the number in base 10 in parentheses after the multibase number:
121 (11)

by **FourTael** » Wed Jan 05, 2011 9:08 pm UTC

Very well.

200 (12)

by **LucasBrown** » Wed Jan 05, 2011 10:30 pm UTC

201 (13)

by **FourTael** » Wed Jan 05, 2011 10:37 pm UTC

210 (14)

by **LucasBrown** » Thu Jan 06, 2011 1:03 am UTC

211 (15)

by **FourTael** » Thu Jan 06, 2011 2:26 am UTC

220 (16)

by **LucasBrown** » Thu Jan 06, 2011 3:41 am UTC

221 (17)

by **FourTael** » Thu Jan 06, 2011 4:10 am UTC

300 (18)

by **APolaris** » Thu Jan 06, 2011 5:08 pm UTC

Wasn't the hundreds place supposed to be base 4?

by **FourTael** » Thu Jan 06, 2011 6:09 pm UTC

Yes, which means it will increase to 1000 after 321. Also, please count along when you reply. Yours was 301 (19).

Mine is 310 (20)

by **coolguy5678** » Thu Jan 06, 2011 6:52 pm UTC

311 (21)

by **FourTael** » Thu Jan 06, 2011 6:56 pm UTC

320 (22)

by **LucasBrown** » Thu Jan 06, 2011 8:49 pm UTC

321 (23)

by **FourTael** » Thu Jan 06, 2011 9:16 pm UTC

1000 (24, aka 4!)

by **LucasBrown** » Fri Jan 07, 2011 1:00 am UTC

1001_! (25₁₀)

by **FourTael** » Fri Jan 07, 2011 1:13 am UTC

1010 (26)

by **pizzazz** » Wed Jan 12, 2011 6:13 am UTC

1011 (27)

As an aside, do we know if it is possible to produce all integers this way?

by **FourTael** » Wed Jan 12, 2011 6:51 am UTC

1020 (28)

Absolutely. I actually designed a similar counting system as a kind of code. It can work off any set of numbers agreed upon beforehand. IE pi * sqrt(14) to the eighth decimal place (or to as many places as the two calculators will show). If there's a 1, as in the example (11.754763358538997856165619429959), then the base would be greater than 10. In the example, it would be 11 (because 1 * 10 + next digit, which is 1).

by **Sean Quixote** » Mon Jan 17, 2011 9:01 pm UTC

Uhm, somebody is wrong here - either one of me or all of you

, yeah, sure makes it seem like it's me, but... From what I understand we're supposed to do, and I'm at least pretty sure that I do, you've all been wrong since the very first post?

Here's the way that I see it:

1₂ - (1₁₀)
10₂ - (2₁₀)
11₂ - (3₁₀)
100₂ - (4₁₀)
101₂ - (5₁₀)
110₂ - (6₁₀)
111₂ - (7₁₀)
1000₂ - (8₁₀)
1001₂ - (9₁₀)
101₃ - (10₁₀)
102₃ - (11₁₀)
110₃ - (12₁₀)
111₃ - (13₁₀)
112₃ - (14₁₀)
120₃ - (15₁₀)
121₃ - (16₁₀)
122₃ - (17₁₀)
200₃ - (18₁₀)
201₃ - (19₁₀)
202₃ - (20₁₀)
210₃ - (21₁₀)
211₃ - (22₁₀)
212₃ - (23₁₀)
220₃ - (24₁₀)
221₃ - (25₁₀)
222₃ - (26₁₀)
1000₃ - (27₁₀)
1001₃ - (28₁₀)

1002₃ - (29₁₀)

Shouldn't it be like this? :?:

by **FourTael** » Mon Jan 17, 2011 10:13 pm UTC

No. Not at all. Your number was 1021 (29). There is no single base for the entire number. It changes by the digit. It's this: 1₅0₄2₃1₂.

My number is 1100 (30).

by **Sean Quixote** » Mon Jan 17, 2011 10:59 pm UTC

Oh. Okay, I might be thinking this is more complicated than it is...

So... Mine is...

1101 (31)

?

by **cjdrum** » Mon Jan 17, 2011 11:12 pm UTC

1102₃ (32)

Wouldn't it make more sense to base the number system of the base 10 number?

by **Sean Quixote** » Mon Jan 17, 2011 11:47 pm UTC

Either I'm comfused yet again, or yours was supposed to be 1110 (32).

Which would make mine 1111 (33).

by **FourTael** » Tue Jan 18, 2011 1:40 am UTC

You got it right, Sean.

CJDrum: It's not a single base for all digits. It's a different base for each digit.

1120 (34)

by **Sean Quixote** » Tue Jan 18, 2011 1:48 am UTC

1121 (35)

by **FourTael** » Tue Jan 18, 2011 1:51 am UTC

1200 (36)

by **Sean Quixote** » Tue Jan 18, 2011 1:55 am UTC

1201 (37)

by **FourTael** » Tue Jan 18, 2011 4:53 am UTC

1210 (38)

by **Sean Quixote** » Tue Jan 18, 2011 9:19 pm UTC

1211 (39)

by **FourTael** » Tue Jan 18, 2011 10:32 pm UTC

by **Sean Quixote** » Tue Jan 18, 2011 11:34 pm UTC

1221 (41)

by **FourTael** » Wed Jan 19, 2011 2:08 am UTC

1300 (42)

by **Sean Quixote** » Wed Jan 19, 2011 2:54 pm UTC

1301 (43)

by **FourTael** » Wed Jan 19, 2011 10:59 pm UTC

by **Sean Quixote** » Thu Jan 20, 2011 3:08 am UTC

1311 (45)

by **FourTael** » Thu Jan 20, 2011 4:01 am UTC

1320 (46)

by **Sean Quixote** » Thu Jan 20, 2011 5:02 am UTC

1321 (47)

by **FourTael** » Thu Jan 20, 2011 7:59 am UTC

2000 (48)

by **Sean Quixote** » Thu Jan 20, 2011 1:41 pm UTC

2001 (49)

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