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To design a power-efficient digital signal processor, this study develops a fundamental arithmetic unit of a low-power adder that operates on effective dynamic data ranges. Before performing an addition operation, the effective dynamic ranges of two input data are determined. Based on a larger effective dynamic range, only selected functional blocks of the adder are activated to generate the desired result while the input bits of the unused functional blocks remain in their previous states. The added result is then recovered to match the required word length. Using this approach to reduce switching operations of noneffective bits allows input data in 2's complement and sign magnitude representations to have similar switching activities. This investigation thus proposes a 2's complement adder with two master-stage and slave-stage flip-flops, a dynamic-range determination unit and a sign-extension unit, owing to the easy implementation of addition and subtraction in such a system. Furthermore, this adder has a minimum number of transistors addressed by carry-in bits and thus is designed to reduce the power consumption of its unused functional blocks. The dynamic range and sign-extension units are explored in detail to minimize their circuit area and power consumption. Experimental results demonstrate that the proposed 32-bit adder can reduce power dissipation of conventional low-power adders for practical multimedia applications. Besides the ripple adder, the proposed approach can be utilized in other adder cells, such as carry lookahead and carry-select adders, to compromise complexity, speed and power consumption for application-specific integrated circuits and digital signal processors.