-2
$\begingroup$

Instead of binary, I need the base $b=0.5$

There is an online tool or an easy software that does change of base to non integer bases?

  • 4
    Is that just base 2 written backwards? What are the possible digits? – 2017-01-29
  • 0
    @haqnatural I have no clue about what you mean. – 2017-01-29
  • 0
    @ Henning Makholm I mean to represent $\sqrt(8)$ in radix 0.5. – 2017-01-29
  • 0
    @CitoEjoy Non-integer bases are unusual. So you should show at an easier example how it works. – 2017-01-29
  • 2
    @CitoEjoy I don't understand how you can take radix less than 1. That means the only allowed digit is 0, which is absurd. – 2017-01-29
  • 0
    @ Henning Makholm Oh, I see what you mean. Integer and fractional parts are inverted. – 2017-01-29

1 Answers 1

1

Following Henning Makholm comment, since the binary expansion of $\sqrt(8)$ is 10.110101000001001111001100110011111110011101111001100100100001000101100101111101100010011011001101110101010010101011111010011110...

then the $\frac{1}{2}$ expansion should be that string inverted. I find weird that it has infinite terms.

I didn't expected some trolls downvoting this just because they ignore the answer. I also would like if I could reward Henning Makholm in some way.

  • 1
    The downvote is due to lack of showing effort and that it is not shown how a base-$\frac{1}{2}$-expansion should work (No, I am not one of the downvoters) – 2017-01-29
  • 0
    If somebody does not knows differential calculus, he shouldn't be downvoting questions about derivatives. The person asking does not should be obliged to explain calculus. My confusion was caused by the impossibility of writing the integer part with positive powers of the radix. Henning Makholm made me notice that negative powers do the work. – 2017-01-29
  • 2
    I don't think the conclusion of your comment above (now deleted as rude) is justified. You still haven't specified what a base $1/2$ expansion means. You are implying that digits should be $0$ and $1$, but that's not a gimme by any means. Also, you should specify the topology (or the metric) in which you expect the convergence to take place. For example, some may take it that the sequence of digits expanding to the left means a $2$-adic topology. But that doesn't work at all, because $\sqrt8$ has no $2$-adic expansion in terms of powers of two (as it generates a ramified extension). – 2017-01-29
  • 0
    A more interesting question might be: how to represent this number in base $\sqrt 2$? – 2017-01-30