In this paper, an electro-optical 4-to-2 encoder based on a photonic crystal is presented. The structure is composed of four silicon waveguides, four photonic crystal structures including the graphene-${{\rm Al}_2}{{\rm O}_3}$Al2O3 stacks, and two optical combiners. Two one-dimensional arrays of air holes in the silicon background are designed parallel to the waveguides. Also, a graphene-${{\rm Al}_2}{{\rm O}_3}$Al2O3 stack is placed at the center of each array, which provides the desired interferences. This feature is used for controlling the optical wave transmission through the waveguides. Using two optical combiners at the end of two waveguides, the received signals from the waveguides will be guided toward the output ports. The amount of the transmitted signal from input ports to the output of the encoder can be controlled by applying the proper chemical potential to the graphene-based stacks. The simulation results show that the encoding operation can be achieved by using 0.2 eV and 0.8 eV for chemical potentials. In addition, the normalized output power margins for logic 0 and 1 are calculated to be 8.2% and 46.7%, respectively. The footprint for the proposed structure is approximately equal to ${127}\;\unicode{x00B5} {{\rm m}^2}$127µm2. Also, the required optical power intensity at input ports is ${100}\;{\rm mW/}\unicode{x00B5} {{\rm m}^2}$100mW/µm2.