Logic gate is the cornerstone of the integrated circuits, digital circuitry, etc. Boolean operations (e.g., and and or logic gates) are recently executed by bistable systems through logical stochastic resonance (LSR), a nonlinear dynamical mechanism that embodies this phenomenon. However, the realization of exclusive-or (xor) and equivalence (xnor) logic gates through LSR remains unresolved in bistable systems. Through the analytical solution and numerical simulation, we here propose a simple scheme for implementing reliable xor and xnor logic gates based on a classical bistable system with the absolute-value of input signals. We verified the stability of the system in terms of various parameters such as mean first passage time, correct probability, and potential well bias. We have also implemented full-adder arithmetic operations through the scheme, demonstrating the promise of application. Our scheme is simple and readily generalizable, therefore forming the basis for the design of more complex logic operations in the future, and providing new perspectives for the development of possible alternative arithmetic logic platforms.

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• Stochastic dynamical systems