I'll not endorse your actual line of argument, but without knowing much about the internals of a 32-bit float, I can confirm that your final answer is correct.

I'll not endorse your actual line of argument, but without knowing much about the internals of a 32-bit float, I can confirm that your final answer is correct. Source: brute force counting in a small C program. Naturally, this might not scale to 64-bits, unless you have lots of time and computing power to spare.