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In an $N$ bit flash ADC, the analog voltage is fed simultaneously to $2^{N}-1$  comparators. The output of the comparators is then encoded to a binary format using digital circuits. Assume that the analog voltage source $V_{in}$ (whose output is being converted to digital format) has a source resistance of $75 \: \Omega$ as shown in the circuit diagram below and the input capacitance of each comparator is $8 \: pF$. The input must settle to an accuracy of $1/2$ LSB even for a full scale input change for proper conversion. Assume that the time taken by the thermometer to binary encoder is negligible.

If the flash ADC has $8$ bit resolution, which one of the following alternatives is closed to the maximum sampling rate?

  1. $1$ megasamples per second
  2. $6$ megasamples per second
  3. $64$ megasamples per second
  4. $256$ megasamples per second
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