In this study, we design and numerically investigate a novel all optical D flip-flop (AODFF) based on linear photonic crystal (LPhC) structure that is composed of optical waveguides using the finite difference time domain (FDTD) method. The proposed structure has the hexagonal close packed of 16×20 circular rods that are suspended in the air substrate with a lattice constant of 606 nm. The plane wave expansion (PWE) method is used to obtain the band diagram for AODFF at an operating wavelength of 1 550 nm. The proposed optical flip-flop achieves a low delay time of 0.2 ps and a high contrast ratio (CR) of 10.33 dB. The main advantage of this design is that the input power as low as 1 mW/μm² is sufficient for its operation, since no nonlinear rods are included. In addition, the footprint of the proposed AODFF is 100 μm², which is smaller compared to the structures reported in the literature, and it has a fast switching frequency of 5 Tbit/s.