The nonlinear response of an optical microresonator is used in a time multiplexed reservoir computing neural network. Within a virtual node approach combined with an offline training through ridge regression, we solved linear and nonlinear logic operations. We analyzed the nonlinearity of the microresonator as a memory between bits and/or as a neural activation function. This is made possible by controlling both the distance between bits subject to the logical operation and the number of bits supplied to the ridge regression. We show that the optical microresonator exhibits up to two bits of memory in linear tasks and that it allows solving nonlinear tasks providing both memory and nonlinearity. Finally, we demonstrate that the virtual node approach always requires a comparison of the reservoirs performance with the results obtained by applying the same training process on the input signal.