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We present designs of all-optical computing circuits, namely, half-full adder/subtractor, de-multiplexer, multiplexer, and an arithmetic unit, based on bacteriorhodopsin (BR) protein coated microcavity switch in a tree architecture. The basic all-optical switch consists of an input infrared (IR) laser beam at 1310 nm in a single mode fiber (SMF-28) switched by a control pulsed laser beam at 532 nm, which triggers the change in the resonance condition on a silica bead coated with BR between two tapered fibers. We show that fast switching of 50 us can be achieved by injecting a blue laser beam at 410 nm that helps in truncating the BR photocycle at the M intermediate state. Realization of all-optical switch with BR coated microcavity switch has been done experimentally. Based on this basic switch configuration, designs of all-optical higher computing circuits have been presented. The design requires 2n-1 switches to realize n bit computation. The proposed designs require less number of switches than terahertz optical asymmetric demultiplexer based interferometer designs. The combined advantages of high Q factor, tunability, compactness and low power control signals, with the flexibility of cascading switches to form circuits, makes the designs promising for practical applications. The design combines the exceptional sensitivities of BR and microcavities for realizing low power circuits and networks. The designs are general and can be implemented (i) in both fiber-optic and integrated optic formats, (ii) with any other coated photosensitive material, or (iii) an externally controlled microresonator switch., Comment: first submitted to JAP Sept. 18th, 2009; 39 pages, 9 figures, 7 tables