This work introduces a novel Error-Optimized Hardware-Efficient Approximate Adder (EOHEAA) tailored for error-resilient computing tasks, where precision can be traded for improvements in energy, delay, and resource efficiency. The EOHEAA adopts a strategic method of controlled error propagation, enabling significant enhancement in accuracy metrics such as Mean Error Distance (MED), Mean Relative Error Distance (MRED), and Normalized MED (NMED), while maintaining minimal hardware overhead. Synthesized on the Artix-7 FPGA using Verilog HDL, EOHEAA achieves up to 38.6% reduction in power consumption, an 34% improvement in critical path delay, and notable savings in logic resources compared to conventional and state-of-the-art approximate adder designs. Comprehensive analysis across 8, 16, and 32-bit configurations further confirms its scalability and robustness, with PDP improvements reaching 71.5% in wider designs. Notably, EOHEAA outperforms several existing designs by achieving the lowest RMSE , minimum EDmax , and the highest accuracy-to-efficiency balance. ASIC-oriented design flow evaluation is further performed using Cadence Genus with predictive standard-cell libraries to analyze area, power, and timing behavior under advanced technology assumptions. To validate its real-world applicability, EOHEAA has been employed in Edge Detection and Color quantization using K-means clustering, both of which demonstrate high-quality outputs under relaxed accuracy constraints. Furthermore, a lightweight CNN-based validation framework is employed to examine the impact of approximate arithmetic on learning-based workloads, demonstrating that EOHEAA preserves inference accuracy while offering tangible energy and performance benefits. These results collectively position EOHEAA as a strong candidate for next-generation approximate arithmetic units in energy-aware image processing and machine-learning accelerators.
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