In the "Big Data" era, a lot of data must be processed and moved between processing and memory units. New technologies and architectures have emerged to improve system performance and overcome the memory bottleneck. The memristor is a technology with both computing and memory capabilities. In-Memory Computing (IMC) can be performed by applying memristors to stateful design methods. The Fast and Energy-Efficient Logic in Memory (FELIX) logic is one of the stateful implementation logics compatible with memristive crossbar arrays. The way computations are performed can be changed to improve performance. Approximate design methods can be applied in error-resilient applications. In error-resilient applications, an acceptable amount of precision is lost while features such as hardware complexity, latency, and energy are improved. In this paper, using these two concepts, an approximate full adder circuit with exact Cout and approximate Sum outputs has been proposed using the FELIX design method for IMC in two different implementation approaches. The applied memristor count in the proposed FELIX-based Approximate Full Adder (FAFA) in the two proposed implementation approaches (FAFA1 and FAFA2) is improved by 14.28% and 28.57%, energy consumption is improved by 73.735% and 81.754%, respectively. The number of computational steps in both approaches is improved by 66.66% compared to the exact FELIX-based full adder. In this paper, two different scenarios are considered for evaluating the FAFA. In the 1st and 2nd scenarios, respectively, for the three and four Most Significant Bits (MSBs), the exact full adder is used, and for the five and four Least Significant Bits (LSBs), the FAFA is used. The results of error analysis and evaluations of the FAFA in three different image processing applications confirmed that FAFA has high accuracy and acceptable performance.

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