THE VERNIER DEVICE AND RESIDUE NUMBER SYSTEMS
AIR FORCE INSTITUTE OF TECHNOLOGY WRIGHT-PATTERSON AFB OH SCHOOL OF ENGINEERING
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Properties of vernier devices and residue number systems are investigated. First, theory for conventional verniers is developed. This theory includes necessary conditions for constructing a vernier device, basic equation describing vernier operation, vernier scale coding sequence, and characteristics of that sequence. Second, properly designed devices, called residue verniers, are shown to provide decimal analog to residue number conversion. The developed device theory includes necessary conditions to prevent ambiguity in the number system, sufficient conditions to prevent ambiguity of scale readings, physical parameters of the device, and coding sequences for the various scales.
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