Accuracy-Exploration Model for Low-Energy and Gates-Free Approximate Adder Compressors

This paper proposes a model for accurately exploring approximate adder compressors (AxAC) utilizing gates-free logic. As case studies, we explore energy-efficient architectures of approximate 3–2 (Ax3-2), 4–2 (Ax4-2), and 5–2 (Ax5-2) adder compressors (AC), focusing exclusively on gates-free in the critical path. This model for the accuracy analysis of AxACs is essential for estimating the optimal arrangements with repetition (AR) of inputs that are the way outputs for these compressors. For instance, the exact 4–2 AC has five inputs (A, B, C, D, and Cin) and three outputs (Cout, Carry, and Sum). Specifically, the Ax3-2 AC generates nine possible architectural-space gates-free AR, the Ax4-2 AC generates 125, and the Ax5-2 AC generates 2, 401 possible output AR. To estimate all output AR, we implemented the accuracy-exploration model in Python. After identifying the best AR, we created a Pareto front addressing the trade-offs between accuracy, energy, and area. The Ax3-2, Ax4-2, and Ax5-2 proposals demonstrate substantial energy and area efficiency improvements while maintaining high accuracy.