We consider the issue of how a simple network with delayed feedback can exhibit complex but desired dynamical behaviors for memory storage and retrieval. We discuss the simplicity-capacity dilemma arising from the requirement of both large capacity and easy implementation in additive networks. We then propose a novel approach based on signal processing delay and show that the interaction of delay, feedback and refractoriness in a simple inhibitory network of three neurons can generate mathematically trackable coexisting periodic patterns. Therefore, a simple and small network with delayed feedback can process a large amount of information, and time lag in our biological or artificial neural nets is useful for information processing. How the connection topology of a large network enhances the network's capacity for memory storage and retrieval remains to be an interesting task.