Photonic integrated circuits with compact design have opened possibilities for the development of optical computing systems; however, the overuse of photonic components in optical designs has slowed the progress of dense integration. In this paper, we propose an ultra-compact optical full-adder based on directed logic and microring resonators. To the best of our knowledge, the proposed structure requires fewer optical components than any other current designs, resulting in a significantly reduced footprint 59.2µm×29.2µm. Also, the proposed structure exhibits a maximum delay time of approximately 10 ps, implying a minimum date rate of 100 GHz. Simulation results by finite-difference time-domain (FDTD) demonstrate the effectiveness and feasibility of the proposed optical full-adder.