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An introductory lecture in a computer architecture or a microprocessor course must deal with the basic CPU-memory-I/O structure. Most lectures are analytical in their approach; a system block diagram is presented and each block is analyzed. An alternative approach is to use a synthesis technique. A requirement for a machine which is to perform some logical or arithmetic operation is given and the blocks necessary to satisfy this requirement are synthesized as the lecture proceeds. This paper describes such a synthesis approach and gives a number of diagrams which show the evolutionary nature of this method of presentation.