The correct answer is 1,065,353,217. You have an off-by-one error in the following line of argument:

> The number of values between the two is 0x3f800000 - 0x00000000 == 0x3f800000

This should be corrected to:

> The number of values between the two is 0x3f800000 - 0x00000000 == 0x3f800001

In general, the number of numbers in the closed integral interval [a, b] is not b-a, but 1+b-a. For example, the closed interval [0,10] contains 11 integers, not 10.

(The above assumes that the original question assumes the floating point number -0 to be outside of [0,1]. Otherwise, you'll have to add 1 more.)