The magnetic switching core is a small, reliable and inexpensive component for digital logic circuits, but conventional core circuits also include a large number of auxiliary semiconductor components. As a result, the cost and reliability of core circuits are not very different from those built entirely with semiconductors. The possibility of building logical systems that use a minimum of nonmagnetic components is examined. Except for the provision of clock-pulse sources, fully integrated magnetic machines are feasible in principle. Suitable circuits must contain provision for gain, memory and unilateral transmission of data. These requirements can be met by taking advantage of the threshold characteristics of ferromagnetic materials that have a rectangular hysteresis loop. Two approaches are selected for consideration. In the first, a binary digit is represented by the remanent state of magnetization of a ferrite core. Upon the application of clack pulses its state can be transferred to adjacent cores by means of electrical interconnections. In the second approach, a binary digit is represented by a discrete flux pattern in a continuous flux conductor. These patterns can be propagated in a step-by-step process through the flux conductor by means of clock pulses. Examples are given of experimental synchronous sequential circuits using commercially available multiapertured cores. The capabilities, limitations and organization of these circuits arc discussed.