Analysis and synthesis of weighted-sum functions

A weighted-sum (WS) function computes the sum of selected integers. This paper considers a design method for WS functions by look-up table (LUT) cascades. In particular, it derives upper bounds on the column multiplicities of decomposition charts for WS functions. From these, the size of LUT cascades that realize WS functions can be estimated. The arithmetic decomposition of a WS function is also shown. With this method, a WS function can be implemented with cascades and adders.