Droplet-based microfluidic logic gates have many applications in diagnostic assays and biosciences due to their automation and the ability to be cascaded. In spite of many bio-fluids, such as blood exhibit non-Newtonian characteristics, all the previous studies have been concerned with the Newtonian fluids. Moreover, none of the previous studies has investigated the operating regions of the logic gates. In this research, we consider a typical AND/OR logic gate with a power-law fluid. We study the effects of important parameters such as the power-law index, the droplet length, the capillary number, and the geometrical parameters of the microfluidic system on the operating regions of the system. The results indicate that AND/OR states mechanism function in opposite directions. By increasing the droplet length, the capillary number and the power-law index, the operating region of AND state increases while the operating region of OR state reduces. Increasing the channel width will decrease the operating region of AND state while it increases the operating region of OR state. For proper operation of the logic gate, it should work in both AND/OR states appropriately. By combining the operating regions of these two states, the overall operating region of the logic gate is achieved. Microfluidics lab-on-chip devices have many applications in diagnostic assays, analytical chemistry, and biosciences. Using droplet-based microfluidic devices may offer various benefits 1. One of the advantages is encapsulating the important fluids as a droplet in order to prevent them from chemical reactions and pollutions. Another advantage of these systems is a better mixing of the reactant inside the droplet and increasing the reaction speed 2. In this manner the sample volume decreases significantly, the cost of operation is reduced drastically, and diagnostic results are obtained in a much shorter time, higher precision, sensitivity, and portability 3. For the droplet-based microfluidic devices, one needs to consider various components such as the valves and the mixers to perform certain functions. Electric, magnetic and thermocapillary forces are some types of forces that are used to control and manipulate fluid in microfluidic circuits 4-6. Thus, these circuits may contain many components that will make their construction complicated. Furthermore, some external equipment such as the permanent magnet or wire coils should be considered 7-11. Additional components limit the portability, scalability and parallel operations. The solution is automation. In electronics, complex operations are obtained using logic gates. Logic gates have many applications like sound and molecular computing 12,13. By analogy to logic gates (in which the pressure can be analogous to the voltage, the flow rate to the electric current and the hydrodynamic resistance to the electrical resistance) one can derive their functionalities for the microfluidics 14,15. Fabricating fluidics devices that are similar to logic circuits, began in the 1960s 16,17. These devices...