LOGIC GATE ARITHMETIC AND QUATERNIONS Page No: 5297-5305

Christopher C. O’Neill

Keywords: Logic Gate Arithmetic, set theory, dimensional gate operators, boolean algebra, quaternions.

Abstract: A new method for Logic Gate Arithmetic is proposed allowing sets to be added, subtracted, multiplied, and divided in an novel way leading to an alternate and expanded appreciation of the Set Theory. An additional eleven Logic Operators are derived from the known operators: AND, OR, NOR, XOR, and XNOR, and their relationships described. Utilizing the principles of Dimensional Gate Operators (DGO), the new operators are shown to be directly related to dimensionality, both higher and lower, and the relationship to the Quaternions is given preliminary treatment.



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