A memristor-based circuit includes a voltage generator that applies a series of voltage pulses to a memristor to progressively change the resistance of the memristor. A comparator: receives an input electrical value; receives an electrical value based on the resistance of the memristor; compares the received values; and, based on the comparison, enables the application of the voltage pulses to the memristor by the voltage generator until a defined condition is satisfied. This circuit can be used to enable the memristor to be programmed to a desired resistance value, such as for use as a non-volatile memory. It can also enable the resistance of one memristor to be replicated to another memristor. By counting the number of applied voltage pulses, the circuit can be used as an encoder or analog-to-digital converter. Other variants of the circuit enable construction of a decoder or digital-to-analog converter, and an authentication circuit.