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We propose a systematic pipelining method for a linear system to minimize power and maximize throughput, given a constraint on the number of pipeline stages and a set of resource constraints. Unlike most existing pipelining approaches, our method takes the number of pipeline stages as one of the constraints and considers the pipelining as an aspect of power minimization. Operations are retimed so that as many operations as possible take common operands as their inputs, using a novel technique called force-directed retiming; operand sharing is then determined, based on list scheduling. Experimental results show that the proposed approach reduces the power consumption of functional units by 27.8% on average and by more than 50% in some cases, compared to the state-of-the-art pipelining and operand sharing techniques.