Error model and the reliability of arithmetic operations

Error detecting and correcting codes are widely used in data transmission, storage systems and also for data processing. In logical circuits like arithmetic operations, arbitrary faults can cause errors in the result. However in safety critical applications, it is important to avoid those errors which would lead to system failures. Several approaches are known to protect the result of operations during software processing. In the same way like transmission systems, coded processing uses codes for fault detection. But in contrast to transmission systems, there is no adequate channel model available which makes it possible to evaluate the residue error probability of an arithmetic operation in an analytical way. This paper tries to close the gap of arithmetic error models by the development of a model for an ordinary addition in a computer system. Thus, the reliability of an addition´s result can be analytically evaluated.