What is the relation between Input Signals, Timebase-oscillator and Measurement time in Frequency counter?
The time base oscillator in a frequency counter is used to set the measurement time.  For convenience most measurement times are in decade increments ranging from 10 seconds down to 1 microsecond or less depending on the counter.  If the measurement time is 1 millisecond, and the input is 2 MHz, then the counter will accumulate 2000 counts. It will display this with the appropriate units to indicate that the input frequency is 2 MHz, for example as 2.000 MHz. If the measurement time is 0.2 seconds, then the counter will accumulate 400,000 counts.  However the counter will need to process this result so that it can correctly display it as a frequency, for example as 2000.00 kHz. This is why most modern counters include microprocessors to allow non-decade measuremnt times as well as for other purposes. In any case, the time base oscillator is not ignored, it still provides the signal to generate the 0.2 second measurement time.