In this paper, a novel design of an ergodic sequential logic cochlear single partition model, which can reproduce a typical nonlinear sound processing function (so-called nonlinear compression) of a mammalian cochlea, is proposed. Analyses show that the model can reproduce fundamental characteristics of the nonlinear compression of the mammalian cochlea. In addition, the model is implemented by a field programmable gate array, and its operation is verified by experiments. It is then shown that the model can be implemented with fewer circuit elements and consumes lower power compared to a standard ordinary differential equation cochlear model. Finally, it is discussed that the results of this paper will be useful in developing a small and low-power cochlear implant that can reproduce nonlinear sound processing functions of the human cochlea.