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All-optical two input parallel logic gates with bacteriorhodopsin (BR) protein have been designed based on nonlinear intensity-induced excited-state absorption. Amplitude modulation of a continuous wave (CW) probe laser beam transmission at 640 nm corresponding to the peak absorption of O intermediate state through BR, by a modulating CW pump laser beam at 570 nm corresponding to the peak absorption of initial BR state has been analyzed considering all six intermediate states in its photocycle using the rate equation approach. The transmission characteristics have been shown to exhibit a dip, which is sensitive to normalized small-signal absorption coefficient (β), rate constants of O and N intermediate states and absorption of the O state at 570 nm. There is an optimum value of β for a given pump intensity range for which maximum modulation can be achieved. It is shown that 100% modulation can be achieved if the initial state of BR does not absorb the probe beam. The results have been used to design low-power all-optical parallel NOT, AND, OR, XNOR, and the universal NAND and NOR logic gates for two cases: 1) only changing the output threshold and 2) considering a common threshold with different β values.