Is there an easy way to find the radix r?

[mr_coffee]

Hello everyone.

I'm suppose to figure out the radix r of these 2 numbers:
(BEE)r = (2699)10; //the 10 means base 10
Of course r has to be 16 because HEX is the only one with A-F
(365)r = (194)10;
Is there an easy way to figure out the radix here or do i just have to convert 194 to each of the bases and see which one works out?
Also if i wnated to convert
310.2 base 4 to octal, would i just divide by 8 as if u were going to convert a decimal to octal or would I first convert it to decimal by this method:
4^2 * 3 + 4^1x1 + 0 + .5 = 52.5 base 10 now divide by 8 and multiply by 1/8 to get the decimal part.

 

[Kenneth Mann]

Not so fast!
Just because a number has Bs and Es in it doesn't mean its Hexadecimal. It could be in any base from "15" up. In fact, I can look at this example and tell its not Hex. Both Decimal and Hex have Even base, thus an "even" number in one base would have to be even in the other. The decimal 2699 is Odd, while 'BEE' in Hex would be even, thus it can't be Hex. You'll have to figure out what it is.

For the (365)r = (194)10, I don't know any direct comparisons (doesn't mean there isn't one, though), but there are a couple of things you can do. First, since it has a '6' in it, the base can be no lower than "7", so start at that. Then, if the first 'digit' found is incorrect you can stop there and eliminate that base. Same with the second, third, etc., so you generally don't have to convert the whole number if it isn't correct. If it is the correct base, you'd wind up converting the whole thing.

Finally, it is easy to convert back and forth between bases 2, 4, 8, 16, etc. Simply find the binary for the first value, then take it into the second. Example:
310.2 in base (4) gives us:

3 => 11, 1 => 01, 0 => 00, and 2 => 10, so we have:

11,01,00.10 ie. "110100.10" and if we group these as an Octal, we have:

110,100.100 so the Octal would be:

64.4

If you wanted the Hex, you'd get:

0011,0100.1000 = 34.8



KM

 

[Kenneth Mann]

That in the second paragraph above holds only when converting to some other base from base ten. Going the other way, the considerations are a little bit different.

KM

 

[mr_coffee]

Awesome, thanks a lot man!

 

[leright]

use polynomial expansion. you can expand out the number 365, for example, with radix r by saying 3*r^2 + 6*r + 5 = 194. Then you simply need to bring everything over to the left of the equation, so you get 3*r^2 + 6*r - 189 = 0. Then just use the quadratic formula to solve for r. :)