This paper gives a very useful treatment of integer division and clarifies the bits you're finding confusing. https://www.microsoft.com/en-us/research/publicati

This paper gives a very useful treatment of integer division and clarifies the bits you're finding confusing. https://www.microsoft.com/en-us/research/publication/division-and-modulus-for-computer-scientists/ https://www.microsoft.com/en-us/research/publication/divisio...