Analytical Error Evaluation and Hardware Implementation of Approximate Negation Circuits

This project presents the design and hardware implementation of an FPGA-based approximate negation circuit for signed arithmetic in two's complement (2'sC) representation. Developed using Verilog HDL in Xilinx Vivado, the proposed design investigates energy-efficient approximate negation techniques that reduce hardware complexity, power consumption, and propagation delay while maintaining acceptable computational accuracy. Conventional exact two's complement negation requires inversion followed by the addition of one, resulting in increased switching activity and hardware overhead. In contrast, the proposed architecture explores approximate negation methods that provide a balanced trade-off between the exact two's complement approach and the simpler one's complement negation technique. The analytical error characteristics of the approximate circuits are evaluated using metrics such as Error Rate (ER), Mean Error Distance (MED), Mean Relative Error Distance (MRED), and Maximum Error (MaxE) to quantify the impact of approximation on computational accuracy. The hardware implementation is synthesized and verified on an FPGA platform, demonstrating reductions in logic utilization, delay, and power consumption compared to conventional implementations. The proposed approximate negation circuit can be seamlessly integrated into approximate arithmetic units such as adders, subtractors, multipliers, and digital signal processing systems, making it suitable for energy-constrained applications including image processing, artificial intelligence, multimedia processing, and edge computing.