A Universal Arithmetic Building Element (ABE) and Design Methods for Arithmetic Processors

The advent of large-scale integration of logic circuits requires the definition of digital computer structure in terms of large functional arrays of logic of very few types. This paper describes a single-package arithmetic processor called the arithmetic building element (ABE). The ABE accepts operands in either conventional or signed-digit radix-r representation and produces signed-digit results, which the ABE can reconvert to conventional form. Radix 16 is chosen for illustrations. Arrays of ABE´s may be arranged to implement unit- time parallel addition, all-combinational multiplication, and more complex functions which are presently computed by subroutines. To facilitate such arithmetic design, a graph model is developed which permits a translation of the given arithmetical algorithm into an interconnection diagram of ABE´s. The design procedure is illustrated by an array for polynomial evaluation. Speed, cost, and roundoff error of the array are considered. A computer program has been written for the automatic translation of the algorithm graph to an interconnection graph, and for the evaluation of the cost and speed for a given polynomial degree and a given precision requirement.