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Arithmetic error codes constitute a class of error codes that are preserved during most arithmetic operations. Effectiveness studies for arithmetic error codes have shown their value for concurrent detection of faults in arithmetic processors, data transmission subsystems, and main storage units in fault-tolerant computers. In this paper, it is shown that the same class of codes is also quite effective for detecting storage errors in both shift-register and magnetic-recording mass memories. Some of the results are more general and deal with properties of arithmetic error codes in detecting unidirectional failures. For example, it is shown that a low-cost arithmetic error code with check modulus A = 2N - 1 can detect any unidirectional failure which affects fewer than N bits. The use of arithmetic error codes for checking of mass memories is further justified since it eliminates the need for hard-core or self-checking code translators and reduces the number of different types of code checkers required.