Recursive Implementation of Voting Networks

Recursive synthesis of digital circuits leads to systematic design methods, reuse of building blocks, and clean mathematical models for circuit cost and delay. Recursive integer and matrix multiplications, and Fourier transform, are familiar examples. In this paper, we show that threshold voters, including the important special case of majority voters, can be synthesized from smaller networks of the same kind in a simple and easily analyzable way. At the end of the recursion, we get to readily-available AND & OR gates, 3-input counters (or full-adders), and majority circuits, which are realizable in a variety of platforms, including emerging atomic-scale digital technologies.