CS255 Spring 2006Practice Midterm 2

The practice exam will appear one week before the exam.

To study for the midterm I would suggest you: (1) Know how to do (by heart) all the practice problems. (2) Go over your notes three times. Second and third time try to see how huch you can remember from the first time. (3) Go over the homework problems. (4) Try to create your own problems similar to the ones I have given and solve them. (5) Skim the relevant sections from the book. (6) If you want to study in groups, at this point you are ready to quiz each other. The practice midterm is below. Here are some facts about the actual midterm: (a) The midterm will be in class Apr 12. (b) It is closed book, closed notes. Nothing will be permitted on your desk except your pen (pencil) and test. (c) You should bring photo ID. (d) There will be more than one version of the test. Each version will be of comparable difficulty. (e) If your cell-phone or beeper goes off you will be excused from the test at that point and graded on what you have done till your excusal. (f) One problem (less typos) on the actual test will be from the practice test.

1. Define and give an example of each of the following combinational circuit terms: size, depth, fan-in, and fan-out.

2. Suppose we want to add the two 4-bit numbers 31 and 17. Show how what the prefix computation of a carry-lookahead adder on these two numbers would look like.

3. Explain how a Wallace-tree multiplier works. Draw a small example.

4. Suppose I have a circuit of size n and depth 5 that I want to simulate on a CREW PRAM with n^1/2 processors give a rough estimate of the run-time as a function of n.

5. Briefly describe the BoxSort algorithm, and give its run-time and number of processors its uses (without proof).

6. Draw a hexagon and label the vertices in order around the perimeter 1 through 6. Add edges {1,4} {3,5}. Using a mental random generator show how the Parallel MIS algorithm would run on this graph.

7. Explain how the timestamp are used in the Asynchronous Choice Coordination problem to ensure an agreement is reached.

8. Show step by step how Euclid's Algorithm will work on the inputs 50 and 30.

9. Give the unique number x mod 30 such that x mod 2= 3, x mod 3 = 5, and x mod 5 = 7.

10. Explain how the modular-exponentiation algorithm from class worked. Give an example.