An Innovative Dynamic Error-Compensation Design for Fixed-Width Square Utilizing Improved Booth-Folding Protocol

In the realm of digital arithmetic, the precision of fixed-width computations is often compromised by inherent limitations such as quantization, rounding, and overflow errors. This paper presents an innovative dynamic error-compensation design for fixed-width square operations that leverages an improved Booth- Folding protocol to mitigate quantization, rounding, and overflow errors. By integrating robust mathematical modeling with an adaptive error-detection mechanism, the proposed approach dynamically compensates for computational inaccuracies inherent in fixed-width arithmetic. Extensive simulations and FPGA implementations demonstrate that the system consistently achieves high performance, with experimental accuracy values reaching up to 99.87% and mean error levels maintained below 0.0015 units. The improved protocol reduces the number of partial products and dynamically adjusts for errors in real time, ensuring that computational throughput and latency remain optimal even under varying load conditions. Furthermore, resource utilization is kept at efficient levels, supporting scalability and energy efficiency. These results validate the effectiveness of the dynamic error-compensation architecture and underscore its potential to significantly enhance precision in digital arithmetic computations. The implications of this work extend to high-performance digital systems, where reliable, real-time processing is critical, and set a new benchmark for error-resilient computational designs.