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

Q5-B-8 points One urn contains two black balls (labeled B1 and B2​) and one white ball.A second urn contains one black ball and two white balls (labeled W1​ and W2​). Suppose the following experiment is performed: One of the two urns is chosen at random. Next, a ball is randomly chosen from the urn. Then a second ball is chosen at random from the same urn without replacing the first ball. a) What is the probability that two balls of different color are chosen? b) Construct the possibility tree with all possible outcomes.

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}.      

Q7-B-8 points A group of 12 students is available. A team of 4 students is to be selected and then arranged in a line for a photo. In how many ways can this be done?

Given: A 16:1 multiplexer has data inputs D0, D1, …, D15, select inputs S3:0, and output Y.  It is implemented using tristate buffers. What is used to enable the tristate buffer that is connected to D5?

Q3- B 8 points Let ​A​ = {a, b, c, d, e, f} and let ​R​ be the relation with digraph with vertex set V and edge set E. Set of Vertices V = {a, b, c, d, e, f} Set of Edges E = {(a,b), (b,a), (a,e), (e,a), (b,e), (e,b), (d,f), (f,d), (c,c)}. Note: (c,c) means a loop from the vertex c to itself, (a,b) means an edge from vertex a to b, etc, . . .  Test this relation for the following properties: reflexive symmetric transitive

Q3- A 8 points Let ​A​ = {2, 5, 8} and let ​R​ be the relation with digraph with vertex set V and edge set E. Set of Vertices V = {2, 5, 8} Set of Edges E = {(2,2), (5,5), (8,8), (2,5), (2,8), (5,8)}. Note: (2,2) means a loop from the vertex 2 to itself, (2,8) means an edge from vertex 2 to 8, etc, . . .  Test this relation for the following properties: reflexive symmetric transitive

A timing diagram is given for inputs to a basic D Flip-Flop. What is the value of the Q output of the D Flip-Flop at time = 1 ns? Assume the delay from inputs changing to output changing is negligible.

Q2-C-7 points Consider the “Divides” Relation on the following set A. A = {1, 2, 4, 5, 10, 15, 20} Draw the Hasse Diagram. (You can list the set of vertices, and edges for this diagram)  

Given: An 8:1 multiplexer has data inputs D0, D1, …, D7, select inputs S2:0, and output Y. Suppose D0 = 1, D1 = 0, D2 = 0, D3 = 0, D4 = 1, D5 = 0, D6 = 1, D7 = 1, S2 = 0, S1 = 1, and S0 = 1.  What is the value of Y?