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We present a theoretical design of an all-optical reconfigurable logic unit based on optically controlled microcavity switches, for realization of all-optical computing circuits. It can execute different logic and arithmetic operations such as half and full adder or subtractor, by only changing the control inputs on the same circuit. Theoretical designs considering bacteriorhodopsin (BR) protein coated microcavities in tree architecture have been presented. The combined advantages of high Q-factor, tunability, compactness, switching of near-IR signals at telecom wavelengths (1310/1550 nm) with low-power control signals, and flexibility of cascading switches to form circuits, makes the designs promising for practical applications. They combine the ultrahigh sensitivity of both BR and microresonators to define a novel paradigm of all-optical computing based on hybrid nanobiophotonic integration.