The authors study the information storage capacity of a simple perceptron in the error regime. For random unbiased patterns the geometrical analysis gives a logarithmic dependence for the information content in the asymptotic limit. In this case, the statistical physics approach, when used at the simplest level of replica theory, does not give satisfactory results. However for perceptrons with finite stability, the information content can be simply calculated with statistical physics methods in a region above the critical storage level, for biased as well as for unbiased patterns.