Count based frequency meter
In general, a digital frequency counter would have a threshold level that it uses to discriminate between zero and one. This could be a set-able threshold or it could be inherent to the hardware, depending on the system. This would convert a sinusoid into a zero or a one (effectively, a square wave), assuming that it is crossing the threshold.



The digital system would have its own oscillator that drives the counter. The counter would count edges from like crossings (rising to rising or falling to falling). The digital counter may do some averaging or some other processing to provide a stable reading or statistics. 

The digital frequency counter's accuracy would be dependent on the accuracy of its oscillator and its precision would be a function of the oscillator's frequency.