A design of time-optimum and register-number-minimum systolic convolvers

We present an optimum bit-parallel/word-sequential systolic convolver. Our design is the best one among the previous many convolvers in the sense that its optimality in time and space performances is simultaneously attained without augmenting any global control, broadcasting, initial-data-preloading, and/or multi-sequential or parallel I/O ports which were allowed in most of the previous designs. As an application of our convolver we give a systolic polynomial divider which can compute the polynomial division in exactly n + O(1) optimum steps on min(n−m, m)/2]+O(1) systolic cells for the division of any degree n polynomial by any degree m polynomial (n m).