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This paper presents the first fully programmable digital cellular design for nanodevice-based computational fabrics. The system has a fully regular structure and consists of a large number of simple functional units called cells. It is programmable, based on a small number of global signals routed from supporting CMOS and associated nanoscale circuitry. The architecture may be adapted to suit a multitude of information-processing paradigms. One example is shown on a two-dimensional (2D) semiconductor nanowire fabric including corresponding circuit-level aspects. Key metrics such as the density and performance are evaluated. It is seen that this digital cellular design may be up to 22 times denser than an equivalent projected 16 nm CMOS version for image-processing applications. High performance is achieved, with megapixel-size images estimated to require only a few microseconds for processing. Possible manufacturing routes and defect tolerance aspects in the context of image-processing applications are also discussed.