In this chapter, we focus on the recent process on memcomputing (memristor + computing) in intrinsic SiO x -based resistive switching memory (ReRAM or called memristor). In the first section of the chapter, we investigate neuromorphic computing by mimicking the synaptic behaviors in integrating one-diode and one-resistive switching element (1D-1R) architecture. The power consumption can be minimized further in synaptic functions because sneak-path current has been suppressed and the capability for spike-induced synaptic behaviors has been demonstrated, representing critical milestones and achievements for the application of conventional SiO x -based materials in future advanced neuromorphic computing. In the next section of chapter, we will discuss an implementation technique of implication operations for logic-in-memory computation by using a SiO x -based memristor. The implication function and its truth table have been implemented with the unipolar or nonpolar operation scheme. Furthermore, a circuit with 1D-1R architecture with a 4 × 4 crossbar array has been demonstrated, which realizes the functionality of a one-bit full adder as same as CMOS logic circuits with lower design area requirement. This chapter suggests that a simple, robust approach to realize memcomputing chips is quite compatible with large-scale CMOS manufacturing technology by using an intrinsic SiO x -based memristor.