Routing an entire VLSI circuit requires partitioning the circuit (routing area) into smaller, localized routing areas. Using non-rectangular, rotated switchbox shapes (and therefore non-Manhattan routing layout) has the potential to simplify the partitioning of the circuit into routable areas and to use 'dead space' on a chip for routing. The method described in this paper for generating non-rectangular, rotated switchboxes borrows ideas from computer graphics.>

The set theory of arithmetic decomposition is a method of 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.>

A two-stage algorithm for fixed point, radix-16 signed-digit division is presented. The algorithm uses two limited precision radix-4 quotient digit selection stages to produce the full radix-16 quotient digit. The algorithm requires a two-digit estimate of the (initial) partial remainder and a three-digit estimate of the divisor to correctly select each successive quotient digit. The normalization of redundant signed-digit numbers requires accommodation of some fuzziness at one end of the range of numeric values that are considered normalized. A set of general equations for determining the ranges of normalized signed-digit numbers is derived. Another set of general equations for determining the precisions of estimates of the divisor and dividend are derived. These two sets of equations permit design tradeoff analyses to be made with respect to the complexity of the model division. The specific case of a two-stage radix-16 signed-digit division is presented. The staged division algorithm used can be extended to other radices as long as the signed-digital number representation used has certain properties.>

The Cascade hardware architecture for high/variable precision arithmetic is described. It uses a radix-16 redundant signed-digit number representation and directly supports single or multiple precision addition, subtraction, multiplication, division, extraction of the square root, and computation of the greatest divisor. It is object-oriented and implements an abstract class of objects, variable precision integers. It provides a complete suite of memory management functions implemented in hardware, including a garbage collector. The Cascade hardware permits free tradeoffs of space versus time.>

Robertson's Theory of Decomposition and Structured Tiling (an IC design technique) are combined in a structured arithmetic circuit design method. This method, extended by a set of inverse operators and a set of multiply operators, is used with computer-aided design tools to automate the design of arithmetic circuits.