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Optimal Single Constant Multiplication Using Ternary Adders
Univ Kassel, Germany.
Linköping University, Department of Electrical Engineering, Computer Engineering. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0003-3470-3911
Linköping University, Department of Electrical Engineering, Computer Engineering. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0001-5739-3544
Univ Kassel, Germany.
2018 (English)In: IEEE Transactions on Circuits and Systems - II - Express Briefs, ISSN 1549-7747, E-ISSN 1558-3791, Vol. 65, no 7, p. 928-932Article in journal (Refereed) Published
Abstract [en]

The single constant coefficient multiplication is a frequently used operation in many numeric algorithms. Extensive previous work is available on how to reduce constant multiplications to additions, subtractions, and bit shifts. However, on previous work, only common two-input adders were used. As modern field-programmable gate arrays (FPGAs) support efficient ternary adders, i.e., adders with three inputs, this brief investigates constant multiplications that are built from ternary adders in an optimal way. The results show that the multiplication with any constant up to 22 bits can be realized by only three ternary adders. Average adder reductions of more than 33% compared to optimal constant multiplication circuits using two-input adders are achieved for coefficient word sizes of more than five bits. Synthesis experiments show FPGA average slice reductions in the order of 25% and a similar or higher speed than their two-input adder counterparts.

Place, publisher, year, edition, pages
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC , 2018. Vol. 65, no 7, p. 928-932
Keywords [en]
Arithmetic; circuits; circuit optimization; digital arithmetic; field-programmable gate arrays (FPGAs); fixed-point arithmetic optimization; mathematics; multiplying circuits; optimization methods
National Category
Telecommunications
Identifiers
URN: urn:nbn:se:liu:diva-149688DOI: 10.1109/TCSII.2016.2631630ISI: 000437029000023OAI: oai:DiVA.org:liu-149688DiVA, id: diva2:1234449
Available from: 2018-07-24 Created: 2018-07-24 Last updated: 2019-06-28

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