In the past five decades, the dynamics of Baker's map in an infinite precision world have been extensively explored. However, the real structure of Baker's map when implemented in a fixed-point arithmetic domain remains unknown. This paper gives an explicit formulation for the quantized Baker's map. We then demonstrate that the maximum in-degree of the functional graph of Baker's map is invariant under any level of fixed-point arithmetic precision. Intriguingly, we observe a self-similarity phenomenon in the functional graph of a specific Baker's map with incremental increases in precision. These findings provide a foundational benchmark for the dynamic analysis and application of Baker's map and its variants in finite precision environments.