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A theoretical model of a microprogram unit is formulated, and the relationship of this model to a form of feedback shift register is developed. The feedback shift-register machine variant has synchronous and asynchronous prototypes. The asynchronous binary feedback shift-register machines realize every fundamental mode asynchronous sequential (finite-state) machine. The synchronous feedback shift-register machine differs from the standard definition by the addition of transitional states to the usual (nontransitional) states, and a single step in the simulation is a move between nontransitional states. When synchronous feedback shift-register machines are generalized in this way, they also become universal components capable of simulating ali finite-state machines.