Recent content by DoctorBinary

Being rational or irrational is a property of a number, not its base. 1/3 is rational in any base. In base 10, it is 1/3 = 0.(3). In base 2, it is 1/11 = 0.(01). (I used parentheses to indicate repeating digits.)

I didn't say you could measure it -- just that it might be irrational. (But I'm getting into "philosophical" issues beyond my expertise I'm afraid.)

I think our inability to draw something of exactly length sqrt(2) is a separate issue. In any case, whatever we do manage to draw, might it not have an irrational length anyhow?

The length is finite -- just our place value representation of it is infinite.

PARI/GP (http://pari.math.u-bordeaux.fr/" .

Is it "The On-Line Encyclopedia of Integer Sequences" you had in mind? It's http://www.research.att.com/njas/sequences/

You add them like you would in base 10, only using base 16 symbols and doing carries for sums >= 16. Your problem is very simple though, since hex symbols and carries >=16 don't occur: 1100 3301 ----- 4401 Converting to binary works similarly, with base 2 symbols and carries for...

Thanks (I thought I was going crazy).

Isn't he just adding the two terms? (2 + sqrt(-1)) + (2 - sqrt(-1)) = 4. (Sorry, the tex formatting was acting weird in preview mode so I ditched it.)

Actually, you're multiplying by the base you're converting to. In this case, we're multiplying a decimal number by 2 to convert to binary. To convert to hex, you would multiply the decimal number by 16; to convert to octal, you would multiply the decimal number by 8.

You could proceed this way, though it would be cumbersome; it requires long division in binary. 339 = 101010011, and 10 = 1010 (you know how to convert to integers so those two conversions are straightforward). Then do the division: 101010011/1010 (Sorry, I tried to put the long division here...

I "promoted" my binary/decimal converter because it's the only one I know of that can handle fractional binary values (to arbitrary precision). I could have pointed the OP to one of those converters that convert directly to IEEE format, but I thought that would have been "cheating." I thought...

The first thing to do is convert 0.46875 to binary; you can do it by hand, or use a binary converter (I have one at http://www.exploringbinary.com/binary-converter/" ): 0.01111. Then, rewrite 0.01111 so it's in normalized binary scientific notation: 1.111 x 2-2. From there, using the definition...

I don't know of any examples either; it just seems natural to me. Of course, I'm looking at this in hindsight with zero and place value at my disposal.

This is the prevailing answer, but it always leaves me unsatisfied. Personally, I think base 6 is the better match: the right hand is the 1s place, and the left hand is the 6s place.