Memristor crossbars were fabricated at 40 nm half-pitch, using nanoimprint lithography on the same substrate with Si metaloxide-semiconductor field effect transistor (MOS FET) arrays to form fully integrated hybrid memory resistor (memristor)/transistor circuits. The digitally configured memristor crossbars were used to perform logic functions, to serve as a routing fabric for interconnecting the FETs and as the target for storing information. As an illustrative demonstration, the compound Boolean logic operation (C AND D) OR (C AND D) was performed with kilohertz frequency inputs, using resistor-based logic in a memristor crossbar with FET inverter/amplifier outputs. By routing the output signal of a logic operation back onto a target memristor inside the array, the crossbar was conditionally configured by setting the state of a nonvolatile switch. Such conditional programming illuminates the way for a variety of self-programmed logic arrays, and for electronic synaptic computing.