• Title/Summary/Keyword: the Quaternary

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Syntheses and realization of Quaternary Galois Field Sum-Of-Product(QGFSOP) expressed 1-variable functions Permutational Literals (치환리터럴에 의한 Quaternary Galois Field Sum-Of-Product(QGFSOP)형 1-변수 함수의 합성과 실현)

  • Park, Dong-Young;Kim, Baek-Ki;Seong, Hyeun-Kyeong
    • Journal of Advanced Navigation Technology
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    • v.14 no.5
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    • pp.710-717
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    • 2010

  • Even though there are 256 possible 1-qudit(1-variable quantum digit) functions in quaternary logic, the most useful functions are 4!=24 ones capable of representing in QGFSOP expressions by possible permuting of 0,1,2, and 3. In this paper, we propose a permutational literal(PL) representation and a QPL(Quaternary PL) gate which use the operands of a multiplicand A and an augend D in $Ax^C$+D(GF4) operation as a control variable of multi-cascaded PLs. And we also present new PL synthesis algorithms to synthesize QGFSOP expressed 24 (1-qudit) functions by applying three PL operators as ab(mutual permutation), + D(addition), and XA (multiplication). Finally architectures, circuits, and a CMOS implementation to realize proposed PL synthesis algorithms for $Ax^C$+D(GF4) functions are presented.

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