We introduce a novel volistor logic gate which uses voltage as input and resistance as output. Volistors rely on the diode-like behavior of rectifying memristors. We show how to realize the first logic level, counted from the input, of any Boolean function with volistor gates in a memristive crossbar network. Unlike stateful logic, there is no need to store the inputs as resistances, and computation is performed directly. The fan-in and fan-out of volistor gates are large and different from traditional memristor circuits. Compared to solely memristive stateful logic, a combination of volistors and stateful inhibition gates can significantly reduce the number of operations required to calculate arbitrary multi-output Boolean functions. The power consumption of volistor logic is computed and compared with the power consumption of stateful logic using the simulation results obtained by LTSpice-when implemented in a 1×8 or an 8×1 crosspoint array, volistors consume significantly less power.