Using flip-flops to store binary numbers for a calculator is feasible, as they can hold the binary representation of inputs like 5 (0101) using NAND flip-flops. The discussion suggests that pressing buttons 0-9 would store the corresponding 4-bit values in four NAND flip-flops. However, the exact design intentions are unclear, leading to a suggestion to consult digital electronics resources, such as Mano's book, for guidance on creating a simple microprocessor. The conversation emphasizes the importance of clarity in design goals for effective implementation. Understanding digital logic fundamentals is crucial for this project.