11-11: Use the multi-output optimization to synthesize the following in product of sums form: fa (a,b,c,d)= Σ (0, 1, 2, 3, 4, 6, 9, 11) + d (8, 12, 14) fp (a,b,c,d) = (1, 3, 4, 6, 9, 11, 12, 14) + d(0, 8, 10) fy (a,b,c,d) Σ (3, 4, 6, 7, 11, 14, 15) + d (1, 9, 12)

Please provide steps for how you got the solution to the problem provided below. I own two umbrellas and keep them either at home or in the office. In the morning I leave my home and head to the office and then come back in the evening. If when I leave either location it is raining, I will grab an umbrella (if available) and carry it with me all the way and then leave it at the destination. I do not relocate the umbrellas for any reason other than using them to move when raining (in other words, if it is not raining, I leave all umbrellas where they are). For simplicity, assume that it rains with probability 0.2 in the morning and with the probability 0.4 in the evening (independently from each other). Model the location of umbrellas as a Markov chain. Give transition matrix and transition diagram. If I have 2 umbrellas at home monday morning, what is the expected number of umbrellas that I will have on Wednesday?Define states as the number of umbrellas at my home in the morning and…

14] Encode Decimal '-124' using Two's Complement. Express your answer in Hex. 15] How much Current is passing through a 470 ohm Resistor that is dropping 3.3 Volts? Express your answer in Decimal with 2 digits of significance.  16] How many Volts are being dropped by a 2.7k Ohm Resistor if it is passing 75uA? Express your answer in Decimal with 2 digits of significance.

4. If we use a digital multimeter to measure the current In the 500 ohm resistor, how much error will there be in the reading and why Is this so.