OK if you don't like negative power I give you an example of positive power that contradict what you said: [The IEEE 754 format description on Wikipedia was a bit confusing - all those negative powers of 2! It really boils down to - if a number can be represented as a sum of powers of 2]
Which is wrong statement. Why, because:
2^100 can be represents by IEEE (2^100 + 1) cannot.