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Given the following circuit: If the inputs are E=1, A=0 and B=0, what is the value of Y?

Given: Suppose you were to properly minimize this function.  Select all of the groups (prime implicants) in the list below that would be circled.

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 = 1, S1 = 0, and S0 = 0.  What is the value of Y?

Given the following circuit: What function is implemented by Y4?

Q6-5 points Which of the following is a negation for “There exists a real number x such that for all real numbers y, xy > y.”  

Given the following circuit: What function is implemented by Y1?

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 D10?

Q4-12 points Write the following argument in logical form. Then use truth tables (only) to determine whether the argument is valid or invalid, justify your answer. If my check arrives in time, I’ll register for fall semester. I’ve registered for fall semester. Therefore, my check arrived in time.

Q6-5 points Which of the following is a negation for “Given any real numbers a and b, if a and b are rational then a/b is rational.”  

Convert 2510 to an 8-bit two’s complement number (ex: “01101110”)