1. Dimension-measuring device comprising: a scale provided with a series of magnetized areas, a sensor capable of being displaced parallel and opposite the scale and provided with a network of magneto-resistive electrodes connected so as to constitute at least one measuring bridge, a circuit for electrically feeding said at least one measuring bridge and to supply at least one value dependent on the at least one output signal to said at least one measuring bridge, said at least one measuring bridge being fed according to a first mode enabling the displacements of said sensor relative to said scale to be detected with a reduced electric consumption through said magneto-resistive electrodes, then according to at least a second mode enabling a finer measuring with a higher electric consumption in response to the detection of an action of said device.