We study the trade-offs between storage/bandwidth and prediction accuracy of neural networks that are stored in noisy media. Conventionally, it is assumed that all parameters (e.g., weight and biases) of a trained neural network are stored as binary arrays and are error-free. This assumption is based upon the implementation of error correction codes (ECCs) that correct potential bit flips in storage media. However, ECCs add storage overhead and cause bandwidth reduction when loading the trained parameters during the inference. We study the robustness of deep neural networks when bit errors exist but ECCs are turned off for different neural network models and datasets. It is observed that more sophisticated models and datasets are more vulnerable to errors in their trained parameters. We propose a simple detection approach that can universally improve the robustness, which in some cases can be improved by orders of magnitude. We also propose an alternative binary representation of the parameters such that the distortion brought by bit flips is reduced and even theoretically vanishing when the number of bits to represent a parameter increases.