Conventional computer suffers from the von Neumann performance bottleneck due to its hardware architecture that non-volatile memory and logic are separated. The new emerging magnetic logic coupling the extra dimension of spin, shows the potential to overcome this performance bottleneck. Here, we propose a novel category of magnetic logic based on diode-assisted magnetoresistance. By coupling Hall effect and nonlinear transport property in silicon, all four basic Boolean logic operations including AND, NAND, OR and NOR, can be programmed at room temperature with high output ratio in one silicon-based device. Further introducing anomalous Hall effect of magnetic material into magnetic logic, we achieve perpendicular magnetic anisotropy-based magnetic logic which combines the advantages of both high output ratio (>103 %) and low work magnetic field (∼1 mT). Integrated with non-volatile magnetic memory, our logic device with unique magnetoelectric properties has the advantages of current-controlled reconfiguration, zero refresh consumption, instant-on performance and would bridge the processor-memory gap. Our findings would pave the way in magnetic logic and offer a feasible platform to build a new kind of magnetic microprocessor with potential of high performance.