We propose all-optical NOT, XOR, XNOR, and NOR logic designs for NRZ-formatted signal at 340 Gbps. For the optical NOT gate, it is proposed to utilize two orthogonally polarized laser sources at the same frequency to induce cross-gain modulation (XGM) in a semiconductor optical amplifier (SOA). For XOR and XNOR logic gates, it is proposed to cross-couple two orthogonally polarized data streams to induce XGM in SOAs, and the output of these two is combined using a polarization controller to form XOR logic operations. Subsequently, XNOR logic operations are implemented by adding a NOT gate in cascade with XOR logic operations. For the realization of NOR logic operations, two data streams having the same polarization, combined and co-propagating with an orthogonally polarized continuous wave laser source, are proposed to excite XGM in SOA.