Alzheimer's Disease (AD) is an irreversible, degenerative condition that, while incurable, can have its progression slowed or impeded. While there are numerous methods utilizing neural networks for AD detection, there is a scarcity of High-performance AD detection chips. Moreover, excessively complex neural networks are not conducive to on-chip implementation and clinical applications. This study addresses the challenges of high misdiagnosis rates and significant hardware costs inherent in traditional AD detection techniques. A novel and efficient AD detection framework based on a recurrent computational strategy is proposed. The framework harnesses an Artificial Neural Network (ANN) embedded within a System on Chip (SoC) to perform sophisticated Electroencephalogram (EEG) analysis. The approach began by employing a reduced IEEE754 single-precision encoding method to hardware-encode the preprocessed EEG data, thereby minimizing the memory storage area. Next, data remapping techniques were utilized to ensure the continuity of the input data read addresses and reduce the memory access pressure during neural network computations. Subsequently, hierarchical and Processing Element (PE) reuse technologies were leveraged to perform the multiply-accumulate operations of the ANN. Finally, a step function was chosen to establish binary classification circuits dedicated to AD detection. Experimental results indicate that the optimized SoC achieves a 70 % reduction in area and a 50 % reduction in power consumption compared to traditional designs. For various neural network models, the detection model proposed in this paper incurs less overhead, with a training speed 3 to 4 times faster than other traditional models, and a high accuracy rate of 98.53 %.