Efforts to combat the 'von Neumann bottleneck' have been strengthened by Resistive RAMs (RRAMs), which enable computation in the memory array. Majority logic can accelerate computation when compared to NAND/NOR/IMPLY logic due to it's expressive power. In this work, we propose a method to compute majority while reading from a transistoraccessed RRAM array. The proposed gate was verified by simulations using a physics-based model (for RRAM) and industry standard model (for CMOS sense amplifier) and, found to tolerate reasonable variations in the RRAMs' resistive states. Together with NOT gate, which is also implemented in-memory, the proposed gate forms a functionally complete Boolean logic, capable of implementing any digital logic. Computing is simplified to a sequence of READ and WRITE operations and does not require any major modifications to the peripheral circuitry of the array. The parallel-friendly nature of the proposed gate is exploited to implement an eight-bit parallel-prefix adder in memory array. The proposed in-memory adder could achieve a latency reduction of 70% and 50% when compared to IMPLY and NAND/NOR logic-based adders, respectively. Index Terms-Resistive RAM (RRAM), majority logic, majority gate, memristor, 1 Transistor-1 Resistor(1T-1R), von Neumann bottleneck, in-memory computing, compute-in-memory, processing-in-memory, parallel-prefix adder This is author's version of the accepted paper. For the published paper, see the 31st IEEE International Conference on Application-specific Systems, Architectures and Processors (ASAP) proceedings in https://ieeexplore.ieee.org/ See Conference presentation (20 min video) at https://asap2020.cs.manchester.ac.uk/paper.php?id=72