In this paper, we present a resistive switching memristor cell for implementing universal logic gates. The cell has a weighted control input whose resistance is set based on a control signal that generalizes the operational regime from NAND to NOR functionality. We further show how threshold logic in the voltage-controlled resistive cell can be used to implement a XOR logic. Building on the same principle we implement a half adder and a 4-bit CLA (Carry Look-ahead Adder) and show that in comparison with CMOS-only logic, the proposed system shows significant improvements in terms of device area, power dissipation and leakage power.