 So, using integer values only, we can also compare numbers of the form ("a" + "b"φ).The above procedure will never result in the sequence "11", since 11φ = 100φ, so getting a "11" would mean we missed a "1" prior to the sequence "11".Start, e.g., with integer = 5, with the result so far being ...00000.00000...φ

Highest power of φ ≤ 5 is φ3 = 1 + 2φ ≈ 4.236067977

Subtracting this from 5, we have 5 − (1 + 2φ) = 4 − 2φ ≈ 0.763932023..., the result so far being 1000.00000...φ

Highest power of φ ≤ 4 − 2φ ≈ 0.763932023... is φ−1 = −1 + 1φ ≈ 0.618033989...