A loopless gray code for minimal signed-binary representations

Abstract

A string . . . a2a1a0 over the alphabet {-1, 0, 1} is said to be a minimal signed-binary representation of an integer n if n = ∑k≥0 ak2k and the number of non-zero digits is minimal. We present a loopless (and hence a Gray code) algorithm for generating all minimal signed binary representations of a given integer n. © Springer-Verlag Berlin Heidelberg 2005.