The qualitative properties of neural networks described by a system of first-order linear ordinary difference equations which are defined on a closed hypercube of the state space with solutions extended to the boundary of the hypercube are investigated. The class of systems considered can easily be implemented in digital hardware. When implemented by a serial processor (e.g., in digital simulations), the presented class of neural networks offers considerable advantages over digital simulations of the differential equations used to represent the continuous-time neural networks considered in previously published work. The applicability of the present results is demonstrated by means of several specific examples. These include pattern recognition applications.<>