The goal of the paper is to design Boolean n-cube architectures that can tolerate node (processor) failures, called fault-tolerant Boolean n-cubes. While a number of such fault-tolerant Boolean n-cube designs have been previously proposed, most of these designs usually require large hardware overhead, which may be not practical in many applications. In this paper, we present a new approach to the design of fault-tolerant Boolean n-cubes that can achieve the same reliability as some previous schemes while requiring less hardware overhead. We first build a fault-tolerant module containing 2m original nodes with k spare nodes, and then construct the fault-tolerant Boolean n-cube by using a number of such modules. In each module, every spare node can replace any other original or spare node failure. Hence, full spare utilization is achieved in each module. Furthermore, the proposed reconfiguration procedure can be done simply and quickly; i.e., only short time overhead is required during reconfiguration.