A theoretical analysis is presented to calculate the signal phase shift and the gain coefficient associated with two-wave mixing in photorefractive crystals subjected to an external electric field. The relative position of the induced-refractive index grating with respect to the fringe pattern of the two input optical beams leads to a coupling effect between the phase and intensity of these beams. An optical logic operation system that is based on photorefractive two-wave mixing is introduced. This system uses the fringe-shifting techniques that are executed by a Mach-Zehnder interferometer. The proposed system configurations are capable of producing all the basic 16 two-operand Boolean functions simultaneously at different output planes.