This paper investigates the application of eXplainable Artificial Intelligence (XAI) in the design of embedded systems using machine learning (ML). As a case study, it addresses the challenging problem of static silent store prediction. This involves identifying redundant memory writes based only on static program features. Eliminating such stores enhances performance and energy efficiency by reducing memory access and bus traffic, especially in the presence of emerging non-volatile memory technologies. To achieve this, we propose a methodology consisting of: 1) the development of relevant ML models for explaining silent store prediction, and 2) the application of XAI to explain these models. We employ two state-of-the-art model-agnostic XAI methods to analyze the causes of silent stores. Through the case study, we evaluate the effectiveness of the methods. We find that these methods provide explanations for silent store predictions, which are consistent with known causes of silent store occurrences from previous studies. Typically, this allows us to confirm the prevalence of silent stores in operations that write the zero constant into memory, or the absence of silent stores in operations involving loop induction variables. This suggests the potential relevance of XAI in analyzing ML models' decision in embedded system design. From the case study, we share some valuable insights and pitfalls we encountered. More generally, this study aims to lay the groundwork for future research in the emerging field of XAI for embedded system design.