The Number SystemThe Unary SystemSlide 3The Binary and Decimal SystemsSlide 5Number System Base OptimizationThe Ternary SystemSlide 8Number Systems with SubtractionSlide 10The Balanced Ternary SystemSlide 12The Chinese Arithmetic SystemSlide 14Works CitedThe Number SystemBy Jonathan MeeThe Unary SystemAn addition only number systemHas only one symbolImpossible signal transmissionsSystem 1 2 4 10 15Unary I II IIII IIIIIIIIII IIIIIIIIIIIIIIIThe Binary and Decimal SystemsAddition and multiplication number systemsTwo symbols in binaryTen symbols in decimalIs binary the optimal system?System 1 2 4 10 15Unary I II IIII IIIIIIIIII IIIIIIIIIIIIIIIBinary 1 10 100 1010 1111Decimal 1 2 4 10 15Number System Base OptimizationMinimize base number width whilebase X number width is held constant.Results in e, or 2.718…Compare ternary to binary baseThe Ternary SystemThree phase componentsThree bit logicSignal transmissions comparable with binary0 1 2 3 4 5Binary 0 1 10 11 100 101Ternary 0 1 2 10 11 12System 1 2 4 10 15Unary I II IIII IIIIIIIIII IIIIIIIIIIIIIIIBinary 1 10 100 1010 1111Decimal 1 2 4 10 15Ternary 1 2 11 101 120Number Systems with SubtractionRoman number systemLimited subtraction and additionRedundant numberingSystem 1 2 4 10 15Unary I II IIII IIIIIIIIII IIIIIIIIIIIIIIIBinary 1 10 100 1010 1111Decimal 1 2 4 10 15Ternary 1 2 11 101 120Roman I II IV X XVThe Balanced Ternary SystemUses addition, subtraction, and multiplicationEasy representation of negativesQuick balancing to powers of threeInherits all the ternary system’s benefitsSystem 1 2 4 10 15Unary I II IIII IIIIIIIIII IIIIIIIIIIIIIIIBinary 1 10 100 1010 1111Decimal 1 2 4 10 15Ternary 1 2 11 101 120Roman I II IV X XVBalanced Ternary1 11 101110111The Chinese Arithmetic SystemA virtual system that focuses on divisionQuick addition, subtraction, and multiplicationGood for compression, encryption, and multiprocessingSystem 1 2 4 10 15Unary I II IIII IIIIIIIIII IIIIIIIIIIIIIIIBinary 1 10 100 1010 1111Decimal 1 2 4 10 15Ternary 1 2 11 101 120Roman I II IV X XVBalanced Ternary1 11 101ChineseArithmeticFor: {9,13}{1,1} {2,2} {4,4} {1,10} {6,2}110111Works CitedHayes, Brian. “Third Base.” American Scientist Nov.-Dec. 2001: 491-492.Dewdney, A. K. The (New) Turing Omnibus. New York: Owl Books, 1993.Brousentsov, N. P., S. P. Maslov, Alvarez J. Ramil, E.A. Zhogolev. “Development of Ternary Computers at Moscow State University.” 2 Feb. 2008. Russian Virtual Computer Museum. 2006. <http://www.computer-museum.ru/english/setun.htm>Knuth, Donald E. The Art of Computer Programing. Ed. Michael A. Harrison. 2nd ed. 2 vols. Reading: Addison-Wesley Publishing Company,
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