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1 Electronics and Telecommunications Quarterly

1 2008

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Two algorithms for obtaining fixed polarity arithmetic expansion representation of quaternary functions

Lozano C. C., Falkowski B. J., Łuba T.

Electronics and Telecommunications Quarterly

2008

Vol. 54, No 2

149-166

Multiple-valued logic has attracted research interests as one way to improve and overcome the limitations encountered in circuits employing two-valued (binary) logic. In particular, much attention has been paid to the three-valued (ternary) and four-valued (quaternary) logic which form the smallest multiple-valued fields. In this article two algorithms for efficient calculation of quaternary fixed polarity arithmetic expansions (QFPAEs) representation of quaternary functions are presented. The first algorithm operates on disjoint cubes array representation of the input function and is suitable for obtaining selected spectral coefficients. The second algorithm starts from QFPAE in polarity zero and is advantageous for deriving either all QFPAE spectra or QFPAE coefficient vector in nonzero polarities. Both algorithms are simple and have high possibilities of parallel implementation. In order to show the advantage of the proposed algorithm, the computational costs for the second algorithm have been derived and compared with the fast transform method. The comparison shows that the algorithm has lower computational cost for generating the complete polarity matrix.