A family of adders

Abstract

Binary carry-propagating addition can be efficiently expressed as a prefix computation. Several examples of adders based on such a formulation have been published, and efficient implementations are numerous. Chief among the known constructions are those of Kogge and Stone and Ladner and Fischer. In this work we show that these are end cases of a large family of addition structures, all of which share the attractive property of minimum logical depth. The intermediate structures allow trade-offs between the amount of internal wiring and the fanout of intermediate nodes, and can thus usually achieve a more attractive combination of speed and area/power cost than either of the known end-cases. Rules for the construction of such adders are given, as are examples of realistic 32b designs implemented in an industrial Ou25 CMOS process.