A device for counting a number of time unit fractions or a number of movement unit fractions of a mobile member (1; 6; A2), the device including (i) a first cam (1) having a first surface (10: (ii) a second surface (20), the second surface being an abutment surface; (iii) a mobile support (4) urged by a spring (R4); (iv) a mobile pawl (3) mounted on the support (4) and urged by a spring (R3) toward the first surface, the pawl (3) being adapted to cooperate with one or the other of the first and second surfaces (10, 20) according to the position of the support (4); and (v) a control system (80) adapted, in a first or non-counting state of the control system, to maintain the support in a first position and, in a second or counting state of the control system, to allow the movement of the support.