Application of Generalized Reed-Muller Expression for Development of Non-Binary Circuits

Semiconductor devices and binary information technology reach their limits set by the atomic size of miniaturization, calculation speed, and the fundamental principle of energy dissipation per bit processing. Therefore, new technologies in logic design and mathematical approaches must be investigated. Application of multiple-valued logic (MVL) in logic design allows developing gates and circuits with more than two stable states. This enables packing an unprecedented high-density of information. Based on this idea, a new technique of the programmable logic arrays (PLA) construction based on MVL units is considered. The unique aspect of this technique is the application of recurrent generalized Reed-Muller expression (GRME) for MVL function representation. The recurrent procedure for this expression's construction is considered and applied in the PLA development. The proposed structure of PLA consists of two blocks that are memory and logic block. In this paper, we also consider the possibility to use the ferroelectrics for the implementation of cells of the memory block of PLA. The development of gates with multi-stable states is possible by the ferroelectrics ability to pin the polarization as a sequence of stable states.