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We present designs of optoelectronic OR, AND, NOR, and NAND logic gates with multiple pulsed pump laser beams based on the photovoltaic response of bacteriorhodopsin (BR) molecules embedded in a polyvinyl matrix coated on ITO. A detailed experimental study of the photovoltaic response reveals that continuous pulsed exposure to 532 nm and 405 nm laser light results in a large photocurrent/photovoltage, due to rapid reprotonation and chromophore reisomerization, taking BR to the ground state in hundreds of nanoseconds. It also helps in sustaining the photovoltage at higher frequencies and in maintaining the shape of the photovoltage. It is shown experimentally that for a pulsed laser beam at 532 nm with peak pump intensity of 1.19 W/cm2, a photovoltage of 50 mV is generated. A detailed numerical simulation of the photovoltaic response of BR has been carried out taking into account all the six states (B, K, L, M, N, and O) in the BR photocycle to ascertain the effect of various parameters such as lifetime of the M-state, the pump pulse-width, pump intensity, lifetime of excited protons, and rate constant of excited protons. Experimental results are in good agreement with theoretical simulations. The present study opens up new prospects for protein-based optoelectronic computing.