The Zeckendorf representation of a number is simply the representation of that number as the sum of distinct Fibonacci numbers. If the number of terms of this sum is minimized, that representation is unique, as also is the representation when the number of terms is maximized.
Bunder, M. & Tognetti, K. (1991). The Zeckendorf representation and the Golden Sequence. The Fibonacci Quarterly: a journal devoted to the study of integers with special properties, 29 (3), 217-219.