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Memristors-based resistive logic computation units are introduced. By controlling the memristors' conditional set operation adaptively to one of the input polarities, bipolar signal multiplication of an input and a stored reference bit is performed by unipolar memristor devices and control switches. The multiplication result is registered in an output nonvolatile memristor so that the computed output can be accessed anytime later on by reading the output memristor's state. A memristive multiplier circuit demonstrates a fast and highly sensitive pattern recognition for highly complex inputs.