[eru]

Arithmetic coding is the industrial strength way to do this, yes!

However, you can do much simpler and still be pretty efficient (and unbiased).

Suppose your range was numbers between 1 to 49 (inclusive).

If you get a number between 1 to 32, you interpret that as 5 bits. If you got a number between 33 to 48, you interpret that as 4 bits (because you have 16 == 2^4 possibilities between 33 to 48). If you hit 49, you just drop everything and sample again.

So if you got 42, like j7ake suggested, that would be 42 - 32 = 10 = 0b1010.

You can generalize this scheme to other numbers of possibilities.