I'm trying to understand how floating point numbers work.

I think I'd like to test out what I know / need to learn by evaluating the following: I would like to find the smallest x such that x + 1 = x, where x is a floating point number.

As I understand it, this would happen in the case where x is large enough so that x + 1 is closer to x than the next number higher than x representable by floating point. So intuitively it seems it would be the case where I don't have enough digits in the significand. Would this number x then be the number where the significand is all 1's. But then I can't seem to figure out what the exponent would have to be. Obviously it would have to be big (relative to 10^0, anyway).