Stochastic resonance (SR) is a phenomenon where the performance of a nonlinear system subjected to noise is better than it is without noise. This phenomenon can be found both in natural and artificial systems, especially in threshold-based systems such as comparators or a population of neurons. As noise always exists and interacts with the system, it is advantageous to design a system that purposefully uses SR to boost its performance. One possible use of SR is in the signal reconstruction. In this application, noise is added to the input signal and is processed by a comparator to produce a 1-bit output signal. This output can be averaged to recover the amplified input signal. In this thesis, three challenges regarding the use of SR in signal reconstruction are addressed. Firstly, to use SR not only to reconstruct the original signal, but also to implement mathematical operators, specifically a multiplier and an adder, that take two or more input signals. Secondly, to define the relevant metric(s) that can be used to measure the performance of the operators. Lastly, to build a system out of the proposed SR-based operators. The SR-based mathematical operators are implemented on the system level with a comparator as its fundamental building block. To analyze the behavior of the operators, formulas for noise and distortion power are derived. MATLAB simulation is then used to verify the theoretical analysis. Finally, these SR-based mathematical operators are used to build a Teager Energy Operator (TEO) for action potentials (APs) detection. An SR-based multiplier and adder can be implemented with the use of an XNOR logic gate and a binary half adder, respectively. The theoretical formulas are successful in predicting the noise and distortion behavior of the operators. In conclusion, it is possible to implement mathematical operators, specifically multipliers and adders, which use noise to boost their performance. The noise and distortion behavior of these operators can be predicted mathematically. Signal-to-noise ratio (SNR) and signal-to-noise-and-distortion ratio (SNDR) are used to measure the performance of the operators. Systems, specifically a TEO, can be built using the SR-based operators.