A digitizing system includes a first plurality of spaced parallel grid conductors and a second plurality of spaced parallel grid conductors orthogonal to the first plurality of spaced parallel grid conductors. The location of a movable coil arranged on a pen or cursor is determined for each plurality of grid conductors coarsely by sampling the voltage induced in one of the grid conductors from a signal applied to the coil to determine whether the coil is above or below this grid conductor. Through careful selection, a very few grid conductors can be sampled to quickly locate the two grid conductors immediately adjacent to the center of the driven coil. The ratio of the voltages present on these two grid conductors is matched against a list of known ratios representing various positions between the two grid conductors.