It is demonstrated that neuromorphic materials designed for computational tasks can be effectively implemented by drawing an analogy with trigger-based systems built upon classical binary elements. Among the most promising approaches in this context are systems that perform computations based on the Residue Number System (RNS). A specific implementation of a trigger-based adder employing the proposed methodology is presented and tested through simulation modeling. This adder utilizes the representation of natural numbers as elements of a subtraction ring modulo P, where P is the product of Mersenne prime numbers. This configuration enables component-wise, independent execution of arithmetic operations. It is further shown that analogous trigger-based systems can be realized using recurrent neural network analogs, particularly those implemented with neuromorphic materials. The study emphasizes that it is possible to construct a neural network, especially one based on neuromorphic substrates, that can perform logical operations equivalent to those executed by conventional binary circuitry. A key challenge in the proposed approach lies in implementing an operation analogous to the carry mechanism employed in classical binary adders. An algorithm addressing this issue is proposed, based on the transition from computations modulo P to computations modulo 2P.