Sign Detection in Residue Number Systems

This paper is concerned with the sign detection problem in residue number systems. The proposed solution is applicable only to nonredundant systems. It is shown that under rather general conditions an explicit, closed formula for the sign function can be obtained. In a special case, when one of the moduli is 2, the sign function becomes an EXCLUSIVE-OR function. A sign detection algorithm is proposed and methods of implementing the algorithm are presented.