Computer Architecture – Discussion

Discussion 1 Instructions

Please choose one of the following options and answer following the guidelines for discussions. The last two are possible interview questions for digital design jobs.

Ben and Alyssa are having an argument. Ben says, “All integers greater than zero and exactly divisible by six have exactly two 1’s in their binary representation.” Alyssa disagrees. She says, “No, but all such numbers have an even number of 1’s in their representation.” Do you agree with Ben or Alyssa or both or neither? Explain.

Ben and Alyssa are having an argument. Ben says, “I can get the two’s complement of a number by subtracting 1, then inverting all the bits of the result.” Alyssa says, “No, I can do it by examining each bit of the number, starting with the least significant bit. When the first 1 is found, invert each subsequent bit.” Do you agree with Ben or Alyssa or both or neither? Explain.

The king receives 64 gold coins in taxes but has reason to believe that one is counterfeit. He summons you to identify the fake coin. You have a balance that can hold coins on each side. How many times do you need to use the balance to find the lighter, fake coin?

The professor, the teaching assistant, the digital design student, and the freshman track star need to cross a rickety bridge on a dark night. The bridge is so shaky that only two people can cross at a time. They have only one flashlight among them and the span is too long to throw the flashlight, so somebody must carry it back to the other people. The freshman track star can cross the bridge in 1 minute. The digital design student can cross the bridge in 2 minutes. The teaching assistant can cross the bridge in 5 minutes. The professor always gets distracted and takes 10 minutes to cross the bridge. What is the fastest time to get everyone across the bridge?