HIGH RADIX SIGNED DIGIT NUMBER SYSTEMS: REPRESENTATION PARADIGMS

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JABERIPOUR G.; GHODSI M.

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Journal: Scientia Iranica Year:2003 | Volume:10 | Issue:4 Page(s): 383-391

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Title

HIGH RADIX SIGNED DIGIT NUMBER SYSTEMS: REPRESENTATION PARADIGMS

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JABERIPOUR G. | GHODSI M. | Issue Writer Certificate

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Abstract

Redundant signed digit number systems are popular in computationally intensive environments, particularly because of their carry-free property, which allows for digit-parallel addition. The time required for addition is particularly important because other arithmetic operations heavily depend on it. Signed digit number systems with high radices are of particular interest because of less memory requirement to represent a given number. But, the time required to perform digit-parallel addition is, by a relatively large coefficient, logarithmically proportional to the radix. Reduction of this coefficient is the prime goal of the study in this paper, where least cost implementations are emphasized. A novel modification to the conventional carry-free addition algorithm for signed digit numbers is presented and the impact of different representations of signed digits on reducing the time required to perform digit parallel addition is investigated.Three representation paradigms are considered, namely, signed-magnitude, two's complement, and one's complement. Following the common practice, and in order to achieve better results, the power- of- two radices is focused upon. With the new algorithm, the time required to derive the transfer digit reduces to a small constant value, which does not depend on the radix.

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APA: Copy

JABERIPOUR, G., & GHODSI, M.. (2003). HIGH RADIX SIGNED DIGIT NUMBER SYSTEMS: REPRESENTATION PARADIGMS. SCIENTIA IRANICA, 10(4), 383-391. SID. https://sid.ir/paper/289514/en

Vancouver: Copy

JABERIPOUR G., GHODSI M.. HIGH RADIX SIGNED DIGIT NUMBER SYSTEMS: REPRESENTATION PARADIGMS. SCIENTIA IRANICA[Internet]. 2003;10(4):383-391. Available from: https://sid.ir/paper/289514/en

IEEE: Copy

G. JABERIPOUR, and M. GHODSI, “HIGH RADIX SIGNED DIGIT NUMBER SYSTEMS: REPRESENTATION PARADIGMS,” SCIENTIA IRANICA, vol. 10, no. 4, pp. 383–391, 2003, [Online]. Available: https://sid.ir/paper/289514/en

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