The author introduces a parallel algorithm for generating thr canonica
l signed-digit expansion of an n-bit number in O(logn) time using O(n)
gates. The algorithm is similar to the computation of the carries in
a carry look-ahead circuit. It is also proven that if the binary numbe
r x + right perpendicular x/2 left perpendicular is given, then the ca
nonical signed-digit recoding of x can be computed in O(1) time using
O(n) gates.