The paper presents novel 2D photonic crystal (PhC) structures comprising of four circular cavities (CCs) that mimic NOR and NAND gates. 2D Finite difference time domain (2DFDTD) method is used for simulation and analysis of optical behavior of the proposed structures considering perfectly matched layers (PML) around the simulation region. Photonic band gap (PBG) and projected band diagram are obtained using plane wave expansion (PWE) method. It is shown that both the structures function with optical inputs of same wavelength and intensity. The proposed NOR and NAND gates are having low operating powers and good contrast ratio. Being universal gates, NOR and NAND allows for Boolean completeness.Implementation of bypass waveguides is a unique feature of the structures proposed in this paper. When the output is LOW, most of the optical power channelizes out of the structure through bypass waveguides, which otherwise, would go into the input ports affecting the input devices or would remain trapped inside the structure resulting in heating. This issue is not touched in the previous literature and in our opinion, being addressed for the first time.