This quote is followed by "If q were not a single digit, then we peeled off too much of the dividend; back up one digit and try again."
q would be larger than one digit with certainty if we were working with chunks of size N+x (with x >= 2). N digits do not necessarily suffice, so N+1 is it, with the caveat that sometimes we have to drop back to the case of just N digits because q turned out to be longer than one digit.
q would be larger than one digit with certainty if we were working with chunks of size N+x (with x >= 2). N digits do not necessarily suffice, so N+1 is it, with the caveat that sometimes we have to drop back to the case of just N digits because q turned out to be longer than one digit.