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We present a theoretical model to analyze all-optical switching by two-photon absorption induced free-carrier injection in silicon 2 × 2 add-drop microring resonators. The theoretical simulations are in good agreement with experimental results. The results have been used to design all-optical ultrafast (i) reconfigurable De-multiplexer/Multiplexer logic circuits using three microring resonator switches and (ii) universal, conservative and reversible Fredkin and Toffoli logic gates with only one and two microring resonator switches respectively. Switching has been optimized for low-power (25 mW) ultrafast (25 ps) operation with high modulation depth (85%) to enable logic operations at 40 Gb/s. The combined advantages of high Q-factor, tunability, compactness, cascadibility, reversibility and reconfigurability make the designs favorable for practical applications. The proposed designs provide a new paradigm for ultrafast CMOS-compatible all-optical reversible computing circuits in silicon.