Journal of Intelligent Computing IHIRRI Soukaina, ERRAMI Ahmed, KHALDOUN Mohamed 8 4 2017 http://www.dline.info/jic/fulltext/v8n4/jicv8n4_1.pdf Sorting is one of the major research topics. It is defined as the process of rearranging a sequence of values. Generally, many applications require implementation of sorting algorithm that can be evaluated according to different criteria related to time complexity. In this paper, we present a new reconfigurable algorithm for sorting binary numbers; based on iterative approach; where the data elements are represented in a binary manner. Our system is based on a systematic mathematical calculation, updated iteratively. The proposed approach offers a useful tradeoff between rapidity of the algorithm and the memory resources. A simulation program has been developed in C++ in order to validate the proposed approach. The complexity of our algorithm according to the number of iterations is O (n) in the worst case. However, the complexity reaches O (log_2 (n)) in the best case.