New implementations of fully connected neural network architecture are explored, and some efficient implementations based on the pulse-density modulation technique are presented. These VLSI circuits are fully programmable, thereby usable in many applications. The architecture is implemented by using two different approaches: analog implementation with switched-capacitor structures and fully digital implementation. The approaches are also compared from the VLSI point of view. The advantage of the switched-capacitor implementation is the small area of a synapse, thus relatively large networks can be implemented. The architecture of the network is also regular, modular, and easy to expand. For the same complexity of network architecture, the digital implementation requires 30% more silicon area, which can be considered quite insignificant. The advantage of the fully digital implementation is good expandability to larger networks. In addition, single circuits can be joined together to form very large networks.