Nonvolatile static random-access memory (NV-SRAM) is a crucial component type for normally-off computing systems. This work proposes a novel 10T2R resistive random-access memory (ReRAM)-based NV-SRAM controller that is aware of redundant bit writes and considers the conditions of redundant bit writes. When data stored in SRAM cells are the same as the data in ReRAM devices, backup can be skipped. Otherwise, backup is performed. As a result, redundant bit-write conditions indicate that energy can be saved when backing up data. Simulations show that as much as 93% of typical energy requirements can be saved when the high resistive state is larger than 10 MΩ. As long as the probability of redundant bit writes is larger than 25%, backup energy saving can be achieved. The ReRAM chip is manufactured with 90 nm CMOS technology and the ReRAM process of the Industrial Technology Research Institute. This design can be applied to L2 and L3 caches.