A coding apparatus includes a fourth layer codebook that shows N number of codes indicating uniquely respective N integers that increment one by one; and first to third layer codebooks that show M number of codes indicating uniquely respective M integers that are a subset of the N integers, and codes a digital signal using any one of the first to fourth layer codebooks. The coding apparatus does not need to do rescaling even when switching one of the first to fourth layer codebooks into another of them.