{"title":"The Synthesis of Boolean Functions Using a Single rrhreshold Element","authors":"I. J. Gabelman","doi":"10.1109/TEC.1962.5219424","DOIUrl":null,"url":null,"abstract":"The synthesis of a threshold element which realizes a desired Boolean function as its output may be accomplished by solving a basic set of linear inequalities. The determination of this basic set is discussed with the aid of a geometric interpretation of such realizable functions on the vertices of a unit N cube. A solution may be obtained to these inequalities by linear programming. In this paper, a method of synthesis which lends itself to rapid and simple hand computation is given.","PeriodicalId":177496,"journal":{"name":"IRE Trans. Electron. Comput.","volume":"29 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1962-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"21","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"IRE Trans. Electron. Comput.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/TEC.1962.5219424","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 21
Abstract
The synthesis of a threshold element which realizes a desired Boolean function as its output may be accomplished by solving a basic set of linear inequalities. The determination of this basic set is discussed with the aid of a geometric interpretation of such realizable functions on the vertices of a unit N cube. A solution may be obtained to these inequalities by linear programming. In this paper, a method of synthesis which lends itself to rapid and simple hand computation is given.
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