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This work describes a novel approach to teach computer organization concepts with extensive hands-on design experience very early in computer science curricula. While describing the proposed teaching method, it addresses relevant questions about teaching VLSI design to students in computer science and related fields. The approach involves the analysis, simulation, design and effective construction of processors. It is enabled by the use of both, VLSI hardware prototyping platforms constructed with reconfigurable hardware and powerful computer aided design tools for design entry, validation and implementation. The approach comprises a 4-hour a week lecture course on computer organization and a 2-hour a week laboratory, both taught in the 3rd semester. In the first two editions of the course, most students have obtained successful processor implementations. In some cases, considerably complex applications such as bubble sort and quick sort procedures were programmed and run in the designed processors.