This paper studies left invertibility of discrete-time linear I/O quantized
linear systems of dimension 1. Quantized outputs are generated according to a
given partition of the state-space, while inputs are sequences on a finite
alphabet. Left invertibility, i.e. injectivity of I/O map, is reduced to left
D-invertibility, under suitable conditions. While left invertibility takes into
account membership in sets of a given partition, left D-invertibility considers
only distances, and is very easy to detect.