A method and apparatus are provided for efficiently operating a round robin arbitration system in a given computer system. The system utilizes a series of banks of requestors and pointer. The banks of requestors and pointers operate on sequential AND-OR-Inverter/OR-AND-Inverter (AOI/OAI) logic to advance the pointer and efficiently select those requestors with pending requests. The use of the AOI/OAI logic circuitry in the banks of requestors and pointers allows for efficient selection and minimization of complex circuitry reducing the overall circuit area.