Methods of operating timers include generating a periodic timing signal having a first frequency that differs from a desired timer frequency (1 KHz) by a first amount. This periodic timing signal having the first frequency can be generated by dividing a frequency of an input clock signal (e.g., 32.768 KHz) by N, where N is a positive integer greater than one. A typical value of N may be 32. The methods also include techniques to inhibit timing error accumulation by switching a frequency of the periodic timing signal from the first frequency to a second frequency that differs from the desired timer frequency by a second amount. This periodic timing signal having the second frequency can be generated by dividing the frequency of the input clock signal by M, where M is a positive integer unequal to N (e.g., M−N equals ±1).