The set theory of arithmetic decomposition

The Set Theory of Arithmetic Decomposition is a method for designing complex addition/ subtraction circuits at any radix using strictly positional, sign-local number systems. The specification of an addition circuit is simply an equation that describes the inputs and the outputs as weighted digit sets. Design is done by applying a set of rewrite rules known as decomposition operators to the equation. The order in which and weight at which each operator is applied maps directly to a physical implementation, including both multiple-level logic and connectivity. The method is readily automated and has been used to design some higher radix arithmetic circuits. It is possible to compute the cost of a given adder before the detailed design is complete.