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A troublesome error has been found in digital data which represents an image renormalized by a computer. The error, which takes the form of anomalous patterns in the switching sequence of certain bits, contributes unnecessary, signal-dependent noise to the-data. Experimental results illustrating this phenomenon are shown and a theoretical model is derived. The model shows that the phenomenon results from a qtiantization or roundoff error inherent in digital renormalization and describes its detailed behavior. A method for rescaling the data which does not lead to the introduction of noise is described.