There's no need to represent fractions of a turn as binary fractions, since you don't ever need more than 1 turn. You can represent fractions of a turn as (pair

There's no need to represent fractions of a turn as binary fractions, since you don't ever need more than 1 turn. You can represent fractions of a turn as (pair of integer) rationals, and round on the rare occasion that the denominator gets too big.