Analysis and Evaluation of Approximate Ripple-Carry Adders in the Presence of a Single Functional Error (SFE)

As widely used in arithmetic circuits (such as a ripple carry adder [RCA]), approximate computing intentionally introduces errors in the design; however, approximate circuits can also experience errors due to external and physical phenomena (such as cosmic rays or a stuck‐at). These errors can be analyzed by their functional nature. This article examines the impact of a single functional error (SFE) in both an approximate cell as well as the entire RCA. The study analyzes exact and approximate cell designs using a state transition diagram‐based approach to understand the relationships between different types of functional error and the expected behavior in all possible scenarios. The article also proposes a probabilistic analysis for an exact RCA, which aligns well with simulation results for several metrics, such as the error rate (ER). Additionally, an error analysis is conducted on the RCA by considering the number of approximate cells and the location of the single erroneous cell. The results and modeling analysis of the exact RCA show that the ER and the mean error distance (MED) for Carry in ( C in ) = 0 are higher than for C in  = 1; furthermore, the MED for an approximate RCA in the presence of an SFE is higher than for the exact RCA. These findings indicate that an approximate RCA affected by an SFE incurs a significantly degraded accuracy as related to the approximate cell type. Finally, the article provides a binary tree‐based analysis to support the comprehensive simulation results for the RCA’s ER using different approximate cells.