According to the coupling-wave theory of quasi-phase-matched linear electro-optic effect, the logical calculation methods of the AND and OR gates with electro-optical composite were proposed based on a single periodically poled lithium niobate. And those of the exclusive-OR gate, half-adder and half-subtractor were further explored based on cascading periodically poled lithium niobate crystal. With the applied electric field fixed at 0.184 KV/mm and 0.368 KV/mm , the influences of the wavelength, the azimuth and the polar angle of light, as well as the temperature of the crystal on the logic output were discussed. It is found that the logical calculation of the above-mentioned basic logic gates can be performed successfully. However, the logical calculation is very sensitive to the temperature, the azimuth and the polar angle. The slight varization of these parameters will lead to the change of the logic output. The calculation scheme can be generalized to applications of more complex basic logic gate, and the various basic logic gates of more than three logic inputs and outputs.