In this paper, we consider and study a new class of variational inclusions called the Cayley Yosida inclusion problem involving XOR operations. By demonstrating the equivalence of our proposed problem to a fixed-point equation, we establish a foundational connection. Based on this fixed-point formulation, we introduce an iterative algorithm aimed at deriving existence and convergence results for the specified problem. Through systematic analysis, we substantiate the theoretical framework supporting the convergence of our proposed algorithm. To illustrate the practical applicability of our findings, we furnish a numerical example using MATLAB, shedding light on the effectiveness and feasibility of the devised approach. This research contributes to the broader understanding of variational inclusions involving XOR operations, offering a new perspective and computational methodology through the exploration of the Cayley Yosida inclusion problem. The developed algorithm not only provides theoretical insights but also demonstrates its practical utility through the presented numerical case, emphasizing the versatility and effectiveness of the proposed solution in tackling real-world problems.