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Errors due to failures in data processing algorithms may be detected and even corrected by employing systematic convolutional codes defined over the fixed-point arithmetic structures supporting the computations. A new class of arithmetic convolutional codes using symbols from the finite ring associated with normal signed arithmetic is based on binary burst-correcting codes and a code's performance in the larger context exceeds that of an underlying basis code. When failures satisfy the usual guard band requirements for the binary code, error correction is possible using an iterative feedback decoder processing syndromes that are defined over the integers modulo a power of two. A class of high rate burst-correcting codes is discussed in more detail and their properties guarantee the detection of the onset of errors. The corrector also contains failure error-detecting capabilities.