Please help ASAP with both 5 and 6 a and b Thanks A sinusoid

Please help ASAP with both #5 and #6 a and b. Thanks!

A sinusoid is sampled as shown in the figure. The red dots represent the signal samples. Is this sinusoid oversampled, sampled at twice the Nyquist rate, or undersampled? Explain the reason for your answer. A capacitor\'s voltage can be represented by the following equation: v(t) = 10 * (1 - e-0.5t). If this voltage is being sampled by an ADC every 0.5 seconds, find: the values of the first eight samples,v[n],where n = 0 to 7. If the ADC is 4 bits with a full scale input of 15 V, find the binary ADC code for each of the eight samples from part a. and fill in the table above.

Solution

5.The signal is under sampled,because as you can see from the figure the distance between 2 sampled points(sampling period) is greater than the half of the original signal period(i.e Nyquist rate),so signal is undersampled less than the nyquist frequency.

6.a and b) Sample v[n] Binary ADC code
0 0 0000(0)
1 2.2120 0010(2)
2 3.9347 0011(3)
3 5.2763 0101(5)
4 6.3212 0110(6)
5 7.1350 0111(7)
6 7.7687 0111(7)
7   8.2623 1000(8)

Resolution of 4 bit ADC=1/2^n=1/16

For 15 V Reference input minimum value it can detect is 15/(16-1)=1 V

So now as it can detect only above 1 V anything ,so if it measures voltage of 6.8 V the adc only detet 6 V as 0.8 is less than 1 ,it will treat as 6 V only ,So the above code is as per this procedure