The physically separated memory and logic units in traditional von Neumann computers place essential limits on the performance and cause increased energy consumption, and hence in-memory computing is required to overcome this bottleneck. Here, a new bipolar memristor based in-memory logic approach is proposed, which is capable of achieving all 16 possible Boolean logic functions in a single device in less than 3 steps. This approach does not require initialization and can facilitate logic cascading, and the calculation taking place in-situ is showcased by 1-bit full adder and 2-bit multiplier with improved efficiency, thus showing a great prospect in future in-memory computing architecture.