# Digit Expansions

 Title: Digit Expansions Authors: Jonas Bayer (jonas /dot/ bayer999 /at/ gmail /dot/ com), Marco David (marco /dot/ david /at/ hotmail /dot/ de), Abhik Pal (apal /at/ ucsd /dot/ edu) and Benedikt Stock (benedikt1999 /at/ freenet /dot/ de) Submission date: 2022-04-20 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. BibTeX: @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 = apr, year = 2022, note = {\url{https://isa-afp.org/entries/Digit_Expansions.html}, Formal proof development}, ISSN = {2150-914x}, } License: BSD License Status: [ok] This is a development version of this entry. It might change over time and is not stable. Please refer to release versions for citations.