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Error-correcting coding schemes devised for binary arithmetic are not in general applicable to BCD arithmetic. In this paper, we investigate the new problem of using such coding schemes in BCD systems. We first discuss the general characteristics of arithmetic errors and define the arithmetic weight and distance in BCD systems. We show that the distance is a metric function. Number theory is used to construct a class of single-error-correcting codes for BCD arithmetic. It is shown that the generator of these codes possesses a very simple form and the structure of these codes can be analytically determined.