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Exploiting computational precision can improve performance significantly without losing accuracy in many applications. To enable this, we propose an innovative arithmetic logic unit (ALU) architecture that supports true dynamic precision operations on the fly. The proposed architecture targets both fixed-point and floating-point ALUs, but in this paper we focus mainly on the precision-controlling mechanism and the corresponding implementations for fixed-point adders and multipliers. We implemented the architecture on Xilinx Virtex-5 XC5VLX110T FPGAs, and the results show that the area and latency overheads are 1% ~ 24% depending on the structure and configuration. This implies the overhead can be minimized if the ALU structure and configuration are chosen carefully for specific applications. As a case study, we apply this architecture to binary cascade iterative refinement (BCIR). 4X speedup is observed in this case study.