The set theory of arithmetic decomposition

Author

Carter, Tony M. ; Robertson, James E.

Author_Institution

Dept. of Comput. Sci., Utah Univ., Salt Lake City, UT, USA

Volume

39

Issue

8

fYear

1990

fDate

8/1/1990 12:00:00 AM

Firstpage

993

Lastpage

1005

Abstract

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

Keywords

digital arithmetic; logic circuits; logic design; many-valued logics; set theory; addition circuit; arithmetic decomposition; connectivity; decomposition operators; equation; inputs; multiple-level logic; outputs; radix arithmetic circuits; rewrite rules; set theory; sign-local number systems; strictly positional; subtraction circuits; weighted digit sets; Adders; Arithmetic; Circuits; Computer science; Costs; Design methodology; Equations; Hardware; Logic; Set theory;

fLanguage

English

Journal_Title

Computers, IEEE Transactions on

Publisher

ieee

ISSN

0018-9340

Type

jour

DOI

10.1109/12.57037

Filename

57037