Hey all,

 

I was thinking the other day, I know it's possible to have, say, base [math]\pi[/math] number systems...but what about base one? Or base smaller-than-one, eg. [math]1/2[/math]? Or negative bases? Or fractional bases? How would one convert to and from those systems?

 

Cheers,

 

Gabe

I've never heard of using base one or a half. Probably don't really exist practically.

 

For base 1 you could have : 1 , 11, 111, 1111, 11111, 111111, etc.. for 1,2,3,4,5,6...?

In base 10 we use exactly 10 symbols i.e. 0,1,2,3,4,5,6,7,8, and9

In base 2 we use 2 symbols i.e. 0, and 1

 

How many symbols would you use in base 0.5?

 

On the other hand, if you wish to use only the symbols 0 and 1 you can have a sort of "base minus a half" with column values n places left of the "decimal point"of (-0.5)^n and on the right of the "decimal" point (-0.5)^-n

 

It gets silly very quickly

If I got the arithmetic right the column headings are

 

-.125; 0.25; -0.5; 1; -2; 4; -8

So 1 through 6 are

1

0.11

1.11

0.01

1.01

0.111

Numbers "bigger" than 1 are fractions.

 

If anyone ever finds a use for this I will be astounded.

base 2i can be quite interesting any poistive negative, imagenary or negative imagenary number can be represented with out a special sign.

I used to think Octal (base 8) was a pretty obscure counting system until I needed a output display for a prototype computer I made and didn`t have any BCD to 7 segment decoder chips and had to use straight decoders and bit 4 as carry, then it all made sense

 

Decimal would have been nicer from a laziness perspective, but after a while I got used to thinking in octal as well.

although I can`t envisage any practical use for a .5 based system???

at least nothing that can`t be performed in another more suitable base.

I seriously doubt there ever will be a use for a 0.5 based system, this was just a question out of curiosity. I once heard that someone had proved that you can make a number system out of any number, so I was wondering if this also applied to fractions and negative numbers. But thanks a lot for the explanation.

 

How do you convert to/from complex based number systems??

 

Cheers,

 

Gabe