"What do you get when you multiply 6 by 9?"

[Starwhip]

The most common answer would be, of course, 54. But in Hitchhiker's Guide to the Galaxy, the answer is 42. Why? I was bored and my friend and I looked this up. It turns out that in base thirteen 5 * 9 = 42. 5*9 = 54 / 13 = 4 remainder 2, or 42. So there you go.

[Superfluous J]

To quote Douglas Adams: "I may be a sorry case, but I don't write jokes in base 13."

[Holo]

To quote Douglas Adams: "I may be a sorry case, but I don't write jokes in base 13."

That's exactly what someone who writes jokes in base 13 would say.

[R0cketC0der]

He doesn't write jokes in base thirteen. He writes them in base A.

[Starwhip]

Here's another idea we had. Is it possible to have a decimal/fraction base? Like base 5/6'ths? Or base 25.2?

[Stargate525]

Here's another idea we had. Is it possible to have a decimal/fraction base? Like base 5/6'ths? Or base 25.2?

I don't... think... so. the base is the number of units you use before adding a digit. You can't add a digit after using a portion of a base. If you did that, you would probably be counting integers of less than one.

That would be weird.

[Starwhip]

Yes, it would be very weird. But is it possible?

And why is it that if you multiply any number in any other base by the "base number" gives you the number in base ten?

(4 remainder 2 base 13 *13 = 54 base ten)

[KerbMav]

Trapped by definition: to go from base 10 to base x you divide by x.

[Red Iron Crown]

No reason the number base can't be a decimal, fraction, or even an irrational number like pi or e. Lots of reasons why it shouldn't be, though.

[peadar1987]

Here's another idea we had. Is it possible to have a decimal/fraction base? Like base 5/6'ths? Or base 25.2?

So long as it was bigger than 1, sure.

Using base 25.2 as an example

1556 would be (6*25.2)+(5*25.2^2)+(5*25.2^3)+(1*25.2^4)

Or 486617.2416

Can't see how that would be in any way useful though!

[Red Iron Crown]

No reason it can't be less than one, either.

[christok]

Here you go: http://conceptualmath.org/challenge/bases.html

And just because it's Knuth: https://dl.acm.org/citation.cfm?id=367233

[Horn Brain]

You can use bases that are <1. They have the weird property that the value of the digit grows to the right, not to the left. You also have to allow improper values into the digits, though (like allowing (11) (0) in base ten for 110.) This makes the representation non-unique, so another rule could be that you can only use 1 or zero in each place. This will give us some weird properties. An alternative would be introducing new symbols for numbers less than the base (You could have a= 1/6, b= 2/6, c= 3/6, d= 4/6).

For your example, base 5/6, we can just calculate the representation of the number in base 6/5 and reflect the digits over the ones place.

1= 1 in all bases, since the ones place is (base)^0. I don't think I care to write what it would be in proper notation. Probably an infinite repeating pattern.

5/6 would be 10 (improper) or something horrible with our new symbols. Easier to just write b+c.

1/5 is 0.a or something horrible with 1's and 0's.

11/6 would be 11.

25/36 would be 100.

55/36 = 25/36 + 5/6 = 110.

It's a damned mess.

Edited March 31, 2014 by Horn Brain