This paper obtains upper and lower bounds for the switching activity on the state lines of a finite state machine (FSM) that is driven with typical input sequences. By exploiting the symmetries between the Hamming distances of state encodings, we obtain tight bounds on the average Hamming distance, which is proportional to the average switching activity and the overall power dissipation of the system. Since these bounds are independent of the state assignment and the actual circuit implementation, they can be used at an early stage of the FSM design to indicate the largest/smallest possible power consumption. The paper also discusses how redundant state encodings can be chosen to decrease power consumption.