Convert 6.562510 to a Q4.4 fixed-point binary number.  Show all 8 bits and the binary point (ex: “0001.1000”). Note: 1/16 = 0.0625; 2/16 = 0.125; 3/16 = 0.1875; 4/16 = 0.25; 5/16 = 0.3125; 6/16 = 0.375; 7/16 = 0.4375; 8/16 = 0.5; 9/16 = 0.5625; 10/16 = 0.625; 11/16 = 0.6875; 12/16 = 0.75; 13/16 = 0.8125; 14/16 = 0.875; 15/16 = 0.9375

Q4-B-7 points We are given an urn with three balls: two blue balls labeled B1B_1​ and B2B_2​, and one white ball labeled WW. A ball is drawn, replaced, and then another ball is drawn and its color recorded. Let B1WB_1W represent the outcome where the first ball drawn is B1B_1​ and the second ball drawn is WW. Since the ball is returned to the urn before the second is draw, each outcome is equally likely. List all nine possible outcomes of this experiment.     

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.

Given: 101010102  is an 8-bit unsigned binary number. What is its value in decimal (ex: “-25”, “45”)

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