Algorithms for Generating Binary Reflected Gray Code Sequence: Time Efficient Approaches

Abstract

In this paper, we propose two algorithms for generating a complete n-bit binary reflected Gray code sequence. The first one is called Backtracking. It generates a complete n-bit binary reflected Gray code sequence by generating only a sub-tree instead of the complete tree. In this approach, both the sequence and its reflection for n-bit is generated by concatenating a “0” and a “1” to the most significant bit position of the n-1 bit result generated at each leaf node of the sub-tree. The second one is called MOptimal. It is the modification of a Space and time optimal approach [8] by considering the minimization of the total number of outer and inner loop execution for this purpose. In this method, both a sequence and its reflection for n-bit is also generated during each inner loop execution instead of generating only one sequence by adding “0” and “2n-1” to the previous n-1 bit sequence. Finally, we evaluate the performance of the proposed and existing algorithms by measuring the execution time with respect to number of bits and compare the results with each other. Simulation results demonstrate that Backtracking takes small execution time up to 10 bits with maximum improvement of 17.02%. The evaluation also demonstrates that MOptimal also takes small execution time for more than 15 bits showing an improvement of 2.10% for 23 bits.