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Universal modules are presented that can be used to realize any single input-single output synchronous sequential machine in the form of a circuit in which the input signal enters only one module. Additionally, no signal in the circuit fans out to more than some bounded number of terminals where the bound depends only on the module being used. Two different realization schemes are presented. The first scheme is based on the single feedback loop circuit model. Modules are connected in a highly regular array. Inputs to the last row of the array are constant logic signals. In the second scheme, a tree of modules is connected at the back to one or more one-hot reaiizations of a machine closely related to the machine being realized. The first scheme has the advantage of yielding a circuit with a highly regular interconnections pattern. The second scheme generally requires fewer modules. The theory is easily edxtended to machines with more than one input and output.