All-optical synchronous and asynchronous binary up counters that employ silicon micro-ring resonator-based T flip-flops are proposed. An alternative approach to design all-optical synchronous and asynchronous binary up counters is also demonstrated using fewer optical components. The proposed design is theoretically realized in MATLAB simulation software at a very high operational speed of 260 Gbps. The performance of this design is validated through amplitude difference, contrast ratio, extinction ratio, amplitude modulation, on-off ratio, etc. The optimized values of the micro-ring resonator are achieved through numerical simulation, which will help to implement the proposed design practically.