The interest in implementing energy-efficient digital circuits using micro and nanoelectromechanical resonator technology has increased significantly over the last decade given their lower energy consumption in comparison to complementary metal oxide-semiconductor circuits. In this thesis, multiple circuit designs based on micro and nanoelectromechanical beam resonators are presented. These circuits include a nano resonator-based flash style analog-to-digital converter, a 4-bit digital-to-analog converter, and a micro-resonator-based 7:3 counter, all among the key building blocks of a microcomputing system. Simulations and experimental results were obtained for all circuits. In general, the proposed circuits based on nanoelectromechanical resonators show up to 90% reduction in energy consumption compared to their complementary metal-oxide-semiconductor counterparts in MHz operation speeds, fulfilling requirements for many applications such as Internet of Things and biomedical devices.