Which is the first integer that an IEEE 754 float is incapable of representing exactly?

Question

For clarity, if I\'m using a language that implements IEE 754 floats and I declare:

float f0 = 0.f;
float f1 = 1.f;

...and then print them

Answer 1

The largest value representable by an n bit integer is 2ⁿ-1. As noted above, a float has 24 bits of precision in the significand which would seem to imply that 2²⁴ wouldn't fit.

However.

Powers of 2 within the range of the exponent are exactly representable as 1.0×2ⁿ, so 2²⁴ can fit and consequently the first unrepresentable integer for float is 2²⁴+1. As noted above. Again.