Computing Division Using Single-Electron Tunneling Technology

Emerging nanotechnologies, like single-electron tunneling (SET) technology, possesses properties that are fundamentally different from what CMOS offers to engineers. This opens up avenues for novel computational paradigms, which can perform arithmetic operations efficiently by utilizing these new available properties. In this line of reasoning, in this paper we investigate the implementation of division in SET technology using a novel computation paradigm called electron counting. First, we present two schemes that are based on sequential approximation of the quotient. The first scheme is basic and simple to build, but suffers from overshoot and has a rather large delay. The second scheme, which is a modification of the first one, has a delay logarithmic in the quotient magnitude and the simulation results we present indicate that this scheme works correctly. Finally, we propose a division scheme based on the computation of periodic symmetric functions. Although this scheme requires a varactor for which no nanoscale implementation yet exists and which cannot be directly simulated, it demonstrates the possibilities that nanotechnology, and specifically SET technology, potentially offers as it has a time complexity of O(1).