We present theoretically the construction of the fundamental gates using two injection semiconductor laser diodes by muans of mutual coupling-feedback. Two laser diodes driven by a common monochromatic light beam run chaos while chaotic synchronization between the two lasers is achieved by coupling-feedback. The optoelectronic logic gate is implemented by appropriately synchronizing or de-synchronizing the two chaotic states by modulating the currents. The all-optical logic gate is finally implemented by appropriately synchronizing or de-synchronizing the two chaotic states via the modulators modulating the coupling lights, which is an external optical modulation method. Numerical results validated the feasibility of the method.