We propose a p-i-n diode embedded parallel triple microring resonator (MRR) configuration to simultaneously realize optical OR and AND, or NAND and NOR logic gates using a bias-assisted carrier injection mechanism. The applied bias on the rings induces refractive index change in the intrinsic region through bandfilling, bandgap shrinkage and free carrier absorption effects, leading to intensity variation at the output ports of the MRR due to respective resonant wavelength shift. The optical logic gate operational outputs are represented as the light intensities at the output ports of the MRR with the wavelength of the input optical signal launched into the input port being at the resonant wavelength of the microring resonator, while the operands are represented as the bias applied onto the rings. The proposed microring resonator configuration is theoretically optimized for achieving a high contrast ratio and an optical confinement factor by optimizing the intrinsic region width, applied bias, coupling coefficient between ring-bus waveguide and lifetime of carriers in the intrinsic region.