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Applications involving machine learning and neural networks have become increasingly essential in the AI revolution. Emerging trends in Resistive RAM technologies provide high-speed, low-cost, scalable solutions for such applications. These RRAM cells provide efficient and sophisticated memory hardware structures for machine-learning applications. However, it is difficult to achieve reliable multilevel cell storage capacity in these memory technologies due to the occurrence of soft and hard errors. As these memories can store multi-bits per cell, exploring limited magnitude symbols(multi-bit) error correction in RRAM is important. This paper proposes a new syndrome-based double error correcting code that divides the syndromes into groups and, uses addition and XOR operations to correct double limited magnitude errors in the RRAM cells. The key idea is to use the built-in current summing capability of RRAM cells to perform the addition operations that are used for the error correction thereby greatly reducing the overhead of the decoding logic needed to implement the ECC. This effectively avoids the need for explicit adder hardware in the decoding logic making it smaller and faster than conventional ECC codes with similar error-correcting capability. Experimental results show that the proposed code reduces the number of check symbols and significantly reduces the decoder area and power by using the RRAM cells to perform the addition.