Abstract: A crossbar switch which connects N (N=2.sup.k ; k=0, 1, 2, 3) coarse grain processing elements (rated at 20 million floating point operations per second) to a plurality of memories provides for a parallel processing system free of memory conflicts over a wide range of arithmetic computations (i.e. scalar, vector and matrix). The configuration of the crossbar switch, i.e., the connection between each processing element unit and each parallel memory module, may be changed dynamically on a cycle-by-cycle basis in accordance with the requirements of the algorithm under execution. Although there are certain crossbar usage rules which must be obeyed, the data is mapped over parallel memory such that the processing element units can access and operate on input streams of data in a highly parallel fashion with an effective memory transfer rate and computational throughput power comparable in performance to present-day supercomputers.