Suppose the capacitance in a digital circuit is doubled (the capacitance is now twice what it was before).  If nothing else changed, how does that affect the power consumption?

Q6-B-8 points    In a certain state, all license plates consist of from 4 to 6 symbols chosen from the 26 letters together with the ten digits (0-9) a) How many license plates are possible, repetition allowed ? b) What is the probability that license plates chosen at random have at least one repeated symbol?

Q8-C-8 points a) How many integers from 1 to 1000 are multiples of 2 or 9? b) How many integers from 1 to 1000 are neither multiples of 2 nor multiples of 9?                  

Q9-C-8 points Prove the following Identity:

True of False: A sequential circuit does not have state.

Q1-A-7 points Determine whether the relation , is reflexive, symmetric, transitive, or none and justify your answer: Let denote the congruence modulo 4 relation on the set of integers For all integers

How many D flip-flops are needed to represent 30 different states?

Q13-A-8 points Use Kruskal’s algorithm to find a minimum spanning tree for the following graph. Indicate the order in which edges are added to form the tree. (Enter your answer as a comma-separated list of sets.) The following matrix represents the weighted graph of this question:

Q11-B-8 points Does the following graph have an Euler Circuit? If not, add extra edges to make it an Eulerian Graph. Explain. Set of Vertices V={A,B,C,D,E} Set of Edges E={ AB, AE, AD, AC, BC, BD, BE, CD}.      

Q11-B-8 points Does the following graph have an Euler Circuit? If not, add extra edges to make it an Eulerian Graph. Explain. Set of Vertices V={A,B,C,D,E} Set of Edges E={ AB, AE, AD, AC, BC, BD, BE, CD}.