Title :
A number system with continuous valued digits and modulo arithmetic
Author :
Saèd, Aryan ; Ahmadi, Majid ; Jullien, Graham A.
Author_Institution :
IceFrye Semicond., Kanata, Ont., Canada
fDate :
11/1/2002 12:00:00 AM
Abstract :
This paper presents a novel number system based on signed continuous valued digits. Arithmetic operations in this number system are performed using simple analog circuitry, in contrast to the conventional implementation of arithmetic units by Boolean or multiple-valued logic circuits. Unlike the limited precision offered by classical analog arithmetic circuits, the ensemble of continuous valued digits that comprises a number in this system provides arbitrary implementation precision with standard analog circuitry. The number system also provides almost-carry-free arithmetic structures with digit level redundancy. In this paper, we introduce the mathematical foundations for positive and negative numbers, addition, multiplication, redundancy, radix conversions, and also the digit value integrity for circuit implementations. Potential applications are in the area of low noise and low cross-talk circuitry for arithmetic circuits used in mixed-signal systems.
Keywords :
digital arithmetic; mixed analogue-digital integrated circuits; multivalued logic; addition; almost-carry-free arithmetic structures; analog circuitry; arithmetic circuits; digit level redundancy; digit value integrity; low cross-talk circuitry; low noise circuitry; mathematical foundations; mixed-signal systems; modulo arithmetic; multiplication; negative numbers; number system; positive numbers; radix conversions; signed continuous valued digits; Capacitance; Circuit noise; Crosstalk; Digital arithmetic; Frequency; Logic circuits; Noise level; Noise reduction; Power dissipation; Voltage;
Journal_Title :
Computers, IEEE Transactions on
DOI :
10.1109/TC.2002.1047754