Analog to digital converter question
In integrating type ADC, the conversion takes place in two phases: the run-up phase and the run-down phase. The run-up phase takes a fixed time. But the run-down period depends on the amplitude of input signal. 

So the conversion time depends on input voltage. And the full scale input will take the maximum conversion time.

From wikipedia article on integrating ADC:


  During the measurement of a full-scale input, the slope of the integrator's output will be the same during the run-up and run-down phases. This also implies that the time of the run-up period and run-down period will be equal (\$t_{u} = t_{d}\$) and that the total measurement time will be \$2t_{d}\$. Therefore, the total measurement time for a full-scale input will be based on the desired resolution and the frequency of the controller's clock: 
  $$t_m = 2\frac{2^n}{f_{clk}}$$


From this, it is clear that the maximum input frequency is \$\dfrac{f_{clk}}{2^{n+1}}\$.