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In this paper, we propose a methodology for designing low error efficient approximate adders for FPGAs. The proposed methodology utilizes FPGA resources efficiently to reduce the error of approximate adders. We propose two approximate adders for FPGAs using our methodology: low error and area efficient approximate adder (LEADx), and area and power efficient approximate adder (APEx). Both approximate adders are composed of an accurate and an approximate part. The approximate parts of these adders are designed in a systematic way to minimize the mean square error (MSE). LEADx has lower MSE than the approximate adders in the literature. The 32-bit LEADx with 16-bit approximation has 20% lower MSE than the approximate adder with the lowest MSE in the literature. The 16-bit APEx with 8-bit approximation has the same area, 60% lower MSE, and 4.5% less power consumption in Xilinx Virtex 7 FPGA than the smallest and lowest power consuming approximate adder in the literature. APEx has smaller area and lower power consumption than the other approximate adders in the literature. As a case study, the approximate adders are used in video encoding application. LEADx provided better quality than the other approximate adders for video encoding application. Therefore, our proposed approximate adders can be used for efficient FPGA implementations of error tolerant applications.

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