Design Space Exploration of Binary Arithmetic Circuits and Design of Circuits for Alternative Arithmetic Systems

The purpose of this master's thesis was to explore the circuit design space (speed, area, power) of conventional binary arithmetic and to suggest improvements or alternatives to this arithmetic. The alternatives to the binary arithmetic focused on was the Signed-Digit (SD) number system, the Residue Number System (RNS) and the combination of these two systems (RNS+SD). The work resulted in new and more efficient RNS+SD circuits (modulo adders, multipliers and converters), and a design space mapping of many popular binary 2's-complement circuits. Sammanfattning Syftet med detta examensarbete var att utforska designrymden (hastighet, area, effekt) för kretsar för konventionell binär aritmetik och att föreslå förbättringar eller alternativ till denna aritmetik. Den alternativa aritmetik som främst utforskades var Signed-Digit (SD), Residue Number System (RNS) samt kombinationen av dessa två system (RNS+SD). Arbetet resulterade i nya och mer effektiva RNS+SD kretsar (modulo-adderare, multiplicerare och konverterare) och en kartläggning av designrymden för många populära binära 2-komplementskretsar. List of Appended Papers This master’s thesis is a summary of the following four papers. References to the papers will be made using the Roman numbers associated with the papers. I. Anders Lindström, Michael Nordseth and Lars Bengtsson, “0.13 μm CMOS Synthesis of Common Arithmetic Units”, Technical Report No. 03-11, Department of Computer Engineering, Chalmers University of Technology, August 2003. II. Anders Lindström, Michael Nordseth and Lars Bengtsson, “VHDL Library of Nonstandard Arithmetic Units”, Technical Report No. 03-01, Department of Computer Engineering, Chalmers University of Technology, August 2003. III. Anders Lindström, Michael Nordseth, Lars Bengtsson and Amos Omondi, “Arithmetic Circuits Combining Residue and Signed-Digit Representations”, in Proceedings of the Eighth Asia-Pacific Computer Systems Architecture Conference (ACSAC'2003) published by Springer-Verlag in Lecture Notes in Computer Science (LNCS) Vol. 2823, Aizu-Wakamatsu City, Japan, Sept. 2003. IV. Anders Lindström, Michael Nordseth, Lars Bengtsson and Amos Omondi, “Contributions to residuenumber-system/signed-digit arithmetic”, May 2003. Submitted for publication.