Distributed Arithmetic (DA) plays a key role in embedding DSP functions in the Xilinx 4000 family ofFPGA devices. In this document the DA algorithm is derived and examples are offered that illustrate itseffectiveness in producing gate-efficient designs. Distributed Arithmetic Revisited... Distributed Arithmetic, along with Modulo Arithmetic, are computation algorithms that performmultiplication with look-up table based schemes. Both stirred some interest over two decades ago but havelanguished ever since. Indeed, DA specifically targets the sum of products (sometimes referred to as thevector dot product) computation that covers many of the important DSP filtering and frequencytransforming functions. Ironically, many DSP designers have never heard of this algorithm. Inspired by thepotential of the Xilinx FPGA look-up table architecture, the DA algorithm was resurrected in the early 90’sand shown to produce very efficient filter designs [1].