Microfluidics is a continuously growing field with potential not only in the fields of medical, chemical, and bioanalysis, but also in the domains of optics and information technology. Here, a pressure-driven 3D microfluidic chip is demonstrated with multiple logic Boolean functions. The presence and absence of fluid at the output of the gates represent the binary signals 1 and 0, respectively. Therefore, the logic gates do not require a specially functionalized liquid to operate. The chip is based on a multilevel of poly(methyl methacrylate) (PMMA)-based polymeric sheets with aligned microchannels while a flexible polyimide-based sheet with a cantilever-like structure is embedded to enable a one-directional flow of the liquid. Several Boolean logic functions are realized (AND, OR, and XOR) using different fluids in addition to a half adder digital microfluidic circuit. The outputs of the logic gates are designed to be at different heights within the 3D chip to enable different pressure drops. The results show that the logic gates are operational for a specific range of flow rates, which is dependent on the microchannel dimensions, surface roughness, and fluid viscosity and therefore on their hydraulic resistance. The demonstrated approach enables simple cascading of logic gates for large-scale microfluidic computing systems.