Design Methods for Symmetric Function Generators Based on Threshold Elements

摘要

This paper presents two design methods for threshold element (TE)-based symmetric function generators (SFGs). SFGs enable reconfigurable devices to be more economical by using fewer elements and configuration variables, as compared with lookup tables in conventional field-programmable gate arrays. The first method generates an SFG that consists of $(n + 2)$ TEs and that utilizes $(n + 1)$ configuration variables for any symmetric function of $n$ input variables. The second method successfully reduces the number of TEs because it allows each TE to utilize more configuration variables. This SFG consists of ${lceil 2(n + 1)/3rceil + 1}$ TEs and utilizes $lfloor 4(n + 1)/3rfloor$ configuration variables. There is a tradeoff between the number of TEs and configuration variables in these two SFGs. This tradeoff is discussed in relation to circuit performance.