A system for processing arithmetic information wherein the residue number system is used to partition a calculation into several simpler calculations each of which can be processed in parallel with complete independence. These segments are computationally simple such that all the arithmetic interactions can be ennumerated as mathematical "mappings". By routing signals through various "mappings" a number is encoded into residue form, processed in various ways, and eventually decoded back to a normal number system. The signals are routed in a manner to reflect calculations involving a plurality of operands and operations. By routing several signals in close sequence, calculations are pipelined. By routing different types of signals independently several calculations are carried out substantially simultaneously with each other. Detection of abnormalities in the signal from a given segment is used to exclude the segment from the decoding process thus preserving the correctness of the overall calculations notwithstanding an error in part of the computation.