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With growing interest in multiprocessor system-on-chip (SoC) designs and the increasing number of multicore designs at the high to medium end of the desktop and server markets, the question arises as to whether there should be convergence of the two concepts. This paper explores design principles for SoC multiprocessors and relates them to more general system requirements. It makes a case for focusing design efforts on symmetric multiprocessor (SMP) SoC designs, which have the best chance of making an impact in a wide range of markets, rather than designs for very specific niches, such as the IBM-Sony-Toshiba Cell processor. If SMP-SoC designs are successful, they could represent the next change in packaging in the general computer market: the next step after the microprocessor. A case is made not only for designing a SMP-SoC alternative to the Cell, but for using such a design as an alternative to an aggressively-pipelined uniprocessor.