We present a two-cell Tantalum oxide-based Memristor Cellular Neural Network (M-CellNN) capable of performing multiple logic operations (AND, OR, XOR) by changing only the initial states of its memristors. This flexible design leverages the dynamic state-change properties of memristors to adjust logic functions. Our results show that this approach significantly broadens the range of achievable logic tasks within a compact architecture, underscoring the potential of memristive elements for versatile and robust circuit designs. Additionally, we examine the impact of non-idealities in coupling weights and initial conditions on the outputs of the network.