By combining the functions of Boolean gates and non-volatile memory, stateful logic may enable significant savings in time and energy for computational processes that can be performed directly in main memory and for data analyses in edge environments. A simple reduction to practice this concept is demonstrated by Borghetti et al. in 2010 via a material implication logic gate comprising two parallel memristors and a conditional write operation. Here, a single physical dual-bit memristor, possessing both bipolar and unipolar resistance switching characteristics and utilizing their operations, is demonstrated. This device responds to a conditional write to perform not only implication but multiple other logic functions when configured with a series resistor and addressed with a specific voltage pulse. The simple circuit structure of this dual-bit memristor allows compact sequential logic cascading along the time dimension without a concern of multiple cell accessing related issues. The sequence of implementing a full-adder is also discussed.