Answer Happy

A. Simulate a 11-stage ring oscillator. Assume all the inverters are identical and the output capacitance is 10fF. Subsequently, show how the frequency changes if the threshold voltage of 1 inverter stage is: (i) 10% higher; (ii) 10% lower, than the nominal value. Explain your observations. B. For the graph shown below, the goal is to divide the nodes of the graph into two sets such that the number of edges common to both the sets is maximized. As discussed in class, this problem can be described as the minimization of the Ising Hamiltonian (H) (with J;=-1) Plot all the distribution of states for all possible values of H. Subsequently, develop a code to randomly sample some nodes. These nodes form 1 set and the unselected nodes form another set. Find H. Repeat this process 100 times and plot the distribution of H observed. What is the minimum value of H observed over all the runs? 19 13 20N 15 14 12 17 18 16 10