The recent idea of logical stochastic resonance is verified in synthetic gene networks induced by non-Gaussian noise. We realize the switching between two kinds of logic gates under optimal moderate noise intensity by varying two different tunable parameters in a single gene network. Furthermore, in order to obtain more logic operations, thus providing additional information processing capacity, we obtain in a two-dimensional toggle switch model two complementary logic gates and realize the transformation between two logic gates via the methods of changing different parameters. These simulated results contribute to improve the computational power and functionality of the networks.