A system for performing digital operations, including a first device configured to transform a digital input into one or more signals, at least one AB ring, the at least one AB ring irreducibly-coupled and configured to include at least three terminals, a second device configured to read a portion of a signal expressed upon two or more of the at least three terminals, and a third device configured to transform the portion of the signal expressed upon two or more of the at least three terminals into a digital output, the third device operationally connected to the second device.