This paper analyzes the multi-digit addition process in the LLaMA-3-8B-Instruct model using a combination of linear probing and logit-lens testing. Similar to human addition, it presents a hierarchical process consisting of four stages: linear decoding of the mathematical structure representation, emergence of core computational features, numeric abstraction of the result, and final solution generation. This suggests that the model relies on internal computation rather than memorization to perform multi-digit addition. The code and data are made publicly available, enhancing reproducibility.