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In this paper a novel technique for detecting and correcting errors in the RNS representation is presented. It is based on the selection of a particular subset of the legitimate range of the RNS representation characterized by the property that each element is a multiple of a suitable integer number m. This method allows to detect and correct any single error in the modular processors of the RNS based computational unit. This subset of the legitimate range can be used to perform addition and multiplication in the RNS domain allowing the design of complex arithmetic structures like FIR filters. In the paper, the architecture of a FIR filter with error detection and correction capabilities is presented showing the advantages with respect to filters in which the error detection and correction are obtained by using the traditional RNS technique.