Basic digit sets for radix representation
David W. Matula · Journal of the ACM · 1982
A fimte set of integer digits D with 0 E D is basic for base 13 ff the set of polynomials ~[D] contains a umque P E ~[D] with P(fl) = i for every mteger t Necessary and sufficient conditions are given for D to be basic for ft.Efficient procedures are exhibited for verifying that D is basic for fl and for computing the P E ~[D] such that P(fl) = i for any l.For digit values in excess ofth© base, it is shown that an infLmte class of basle dtgit sets exists for every base fl with [fl[ >_ 3. Infinite precision radix representations are shown to eXLSt for every real number when D is basic for d, and the inherent redundancy of infinite precision representation is investigated.