Issue No. 01 - January (1968 vol. 17)

ISSN: 0018-9340

pp: 46-54

King-Sun Fu , School of Elec. Engrg., Purdue University, Lafayette, Ind.; Visiting Professor at the University of California, Berkeley, Calif.

Chao-Wei Mow , Purdue University, Lafayette, Ind; Litton Industries, Inc., Guidance and Control Systems Division, Woodland Hills, Calif.

ABSTRACT

This paper deals with input tolerance considerations of a multithreshold threshold element. The concept of a multilevel minus-plus-one model<sup>[9]</sup> of a threshold element is introduced. It is shown that the multilevel minus-plus-one model is equivalent to the zero-one model<sup>[9]</sup> of a multithreshold element. The equivalence is established through a set of defining equations similar to that of a single threshold threshold element. For a nonlinearly separable Boolean function, more than one multithreshold weight threshold vector may exist for its realization, even though the number of thresholds and the sum of the absolute magnitude of all the input weights are the same; i.e., ¿<sup>n</sup><inf>i=1</inf> |w<inf>i</inf>|. From reliability considerations, the optimal synthesis of the multithreshold threshold elements is shown to depend on the magnitudes of max (|T<inf>1</inf>|, |T<inf>k</inf>|) in addition to the minimum number of thresholds needed to realize the Boolean function and the min ¿<sup>n</sup><inf>i=1</inf> |w<inf>i</inf>|. An example is given for illustrative purposes of choosing an optimal realization. For a given margin of operation with the error model assumed, it is shown that one need only work from the normalized set of inequalities. The solution with margins specified is obtained from the optimal solutions of the normalized system of inequalities.

INDEX TERMS

CITATION

King-Sun Fu, Chao-Wei Mow, "Input Tolerance Considerations for Multithreshold Threshold Elements",

*IEEE Transactions on Computers*, vol. 17, no. , pp. 46-54, January 1968, doi:10.1109/TC.1968.5008867