In-memory logic calculations and brain-inspired artificial synaptic neuromorphic computing are expected to solve the limitations of the traditional von Neumann computing architecture. The data processing efficiency of the traditional von Neumann architecture is inherently limited by its physically separated processing and storage units, and thus data transmission besides calculation leads to a limited calculation speed and additional high-power consumption. In addition, traditional digital logic calculations and analog calculations have greater limitations in conversion. Herein, we report a flexible two-terminal memristor based on SiCO:H, which is a porous low-k back-end complementary metal-oxide-semiconductor (CMOS)-compatible material. Due to its low operating voltage (200 mV) and fast response speed (100 ns), it could perform digital memory calculation and neuromorphic calculation simultaneously. The memristor could realize a transition from short-term to long-term plasticity in the process of enhancement and inhibition during neuromorphic calculation, with high biological reality. In digital logic calculations, IMP-based and MAGIC-based logic calculations were verified. In neuromorphic computing, an Ag ion-based conductive filament was introduced. The relationship between the temporal dynamics of the conductance evolution and the diffusive dynamics of the Ag active metal could be modulated by the external programming electric field strength. The synapses and neuron dynamics in biology were faithfully simulated, realizing a transition from short-term to long-term plasticity in the process of enhancement and inhibition, which has high compatibility and scalability, proposing a novel solution for the next generation of computer architectures.