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The paper focuses on the Multi-stAge noise SHaping (MASH) digital delta-sigma modulator (DDSM) that employs multi-moduli (MM-MASH). Different architectures of the MASH DDSM are compared. In particular, it is proven that a higherorder error feedback modulator (EFM) has the same sequence length as a first-order EFM (EFM1) in an MM-MASH. In addition, the method that is required to setup the quantisation moduli of the MM-MASH is introduced. The theory is validated by simulation