A memory controller includes a voltage control module that operates to isolate a target memristor of a memory crossbar array. The voltage control module applies a column voltage to a column line coupled to the target memristor, applies a first row voltage to all row lines not coupled to the target memristor and a second row voltage to a row line coupled to the target memristor, and senses a current through the target memristor to determine a state of the target memristor. The memory crossbar array includes a plurality of column lines, a plurality of row lines, a plurality of memristors, and a plurality of shorting switches. Each memristor is coupled between a unique combination of one column line and one row line. Each shorting switch has a high impedance resistor and a low impedance transistor, and each shorting switch is coupled to an end of a unique row line.