design of differentials

in a differential, the pinion gear is rather smaller than the crown gear. so does torque step-up take place when power is transfered from the pinion to the crown gear ? is the amount by which the multiplication takes place significant ?

Yes, the pinion gear is smaller than the ring gear or the crown wheel. One of the task of the differential is to act as the final gear reduction in the vehicle after the gearbox. It is quite obvious that it will step-up the torque. Look at the rear axle ratio of any car. It is significant.