A Note on Minimal Reed-Muller Canonical Forms of Switching Functions

Kodandapani,; Setlur,

doi:10.1109/tc.1977.1674830

Cited by 11 publications

(2 citation statements)

References 4 publications

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“…A given function can be expressed as the XOR of basic entry; its coefficient is called the RM expansion coefficient [17]. Given an -variable function ( 1 , .…”

Section: Reed-muller Expansionmentioning

confidence: 99%

Function Synthesis Algorithm of RTD-Based Universal Threshold Logic Gate

Yao

Yang

et al. 2015

Journal of Applied Mathematics

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The resonant tunneling device (RTD) has attracted much attention because of its unique negative differential resistance characteristic and its functional versatility and is more suitable for implementing the threshold logic gate. The universal logic gate has become an important unit circuit of digital circuit design because of its powerful logic function, while the threshold logic gate is a suitable unit to design the universal logic gate, but the function synthesis algorithm for the -variable logical function implemented by the RTD-based universal logic gate (UTLG) is relatively deficient. In this paper, three-variable threshold functions are divided into four categories; based on the Reed-Muller expansion, two categories of these are analyzed, and a new decomposition algorithm of the three-variable nonthreshold functions is proposed. The proposed algorithm is simple and the decomposition results can be obtained by looking up the decomposition table. Then, based on the Reed-Muller algebraic system, the arbitrary -variable function can be decomposed into three-variable functions, and a function synthesis algorithm for the -variable logical function implemented by UTLG and XOR2 is proposed, which is a simple programmable implementation.

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“…A given function can be expressed as the XOR of basic entry; its coefficient is called the RM expansion coefficient [17]. Given an -variable function ( 1 , .…”

Section: Reed-muller Expansionmentioning

confidence: 99%

Function Synthesis Algorithm of RTD-Based Universal Threshold Logic Gate

Yao

Yang

et al. 2015

Journal of Applied Mathematics

View full text Add to dashboard Cite

show abstract

“…The approach requires the exhaustive computation of all the 2" possible forms in tenns of "polarity functions" and obviously can not again handle functions with large number of variables.Following the first introduction of CGRM forms, being in Taylor series expansion[l], several schemes of minimization in Taylor series fonn were introduced in 70's[17],(38]. Marinkovic and Tosic[80] have proposed a non-exhaustive search for identifying the minimal CGRM form which allows different minimization criteria to be used.Kodandapani and Setlur(75] modified this approach for the case of minimization in terms of the number of the monoterms. Page [94] used a different modification to the method for minimizing the number of literals appearing in an even number of monotenns…”

mentioning

confidence: 99%