Rapid growth of future information technology depends on energy‐efficient computation and ultra‐high density data storage. Non‐volatile redox‐based resistive switching memory (ReRAM) devices offer logic‐in‐memory capabilities and can redefine the von Neumann computer architecture. Especially complementary resistive switches (CRSs) enable the integration of highly dense passive nano‐crossbar arrays in 4F2 structure (F is the minimum feature size) without the need of selector devices. To reduce fabrication complexity further, single ReRAM device in complementary switching (CS) mode is a viable option. Here, the implementation of in‐memory‐adders using Pt|HfO2|Hf|Pt‐based CS devices, which are integrated into 1 × n passive crossbar arrays, is reported. First, the feasibility of all CRS‐logic functions with these CS devices is shown, which offer high‐endurance (109 cycles) under pulse conditions. Afterward, two multi‐bit crossbar adders, the Toggle‐Cell Adder and the Pre‐Calculation Adder, are experimentally demonstrated under pulse conditions realizing addition and subtraction operations. These results prove the functional efficiency of the crossbar adder approach, paving the path for highly advanced ReRAM‐based computing‐in‐memory architectures.