### Abstract

We formalize how a natural number can be expanded into its digits in some base and prove properties about functions that operate on digit expansions. This includes the formalization of concepts such as digit shifts and carries. For a base that is a power of 2 we formalize the binary AND, binary orthogonality and binary masking of two natural numbers. This library on digit expansions builds the basis for the formalization of the DPRM theorem.

### License

BSD License

### Topics

- Mathematics/Number theory

### Session Digit_Expansions

- Bits_Digits
- Carries
- Binary_Operations

### Used by

- Diophantine Equations and the DPRM Theorem

## Cite

×

Digit_Expansions-AFP

    @article{Digit_Expansions-AFP,
      author  = {Jonas Bayer and Marco David and Abhik Pal and Benedikt Stock},
      title   = {Digit Expansions},
      journal = {Archive of Formal Proofs},
      month   = {April},
      year    = {2022},
      note    = {\url{https://isa-afp.org/entries/Digit_Expansions.html},
                 Formal proof development},
      ISSN    = {2150-914x},
    }

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