[rcfox]

You're conflating the magnitudes. You can't directly compare the number of multiplications with the number of transistor switches or CPU cycles required for a single multiplication.

Also, the number n has O(log(n)) digits.

[stephencanon]

The number n has O(log(n)) digits, but that has nothing to do with the subject at hand. The nth fibonacci number has O(n) digits.

And nothing in my comment relates to "number of transistor switches or CPU cycles required for a single multiplication".