Numbers are represented as binary arrays in computer storage. We propose a length-n binary representation of numbers from 0 to 2ⁿ-1 based on Hamming distances such that for any i ∈ {0, ..., 2ⁿ-1}, if a constant number of bits (out of n) are flipped, the normalized L1 distance from the distorted number ierror to i is vanishing when n tends to infinity. More precisely, maxi[(|ierror-i|)/(2ⁿ)]=o([1/(√n)]). A pair of encoder and decoder with O(n) time complexity is presented to establish the Hamming-distance-based bijection between {0,1}ⁿ and {0,1,...,2ⁿ-1}.