Stochastic resonance (SR) is a phenomenon in which noise can be employed to increase the performance of a system. It can e.g. be used to improve the performance of comparator-based circuits. This paper presents the analytical derivation of input-output relation, harmonic distortion, and noise behaviour of a 1-bit ADC using SR. Furthermore, the design of a new signal multiplier based on SR-ADCs is presented. The predicted behaviours are demonstrated by means of simulations. The work presented in this paper shows the potential for analog to digital conversion and integrated signal processing fully based on stochastic resonance.