# CSC3171 Quiz 4Fall 2011

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This is the fourth weekly quiz to be taken on of before the start of on or before Thursday, 27 September 2011. You should do it after you read the first third of Knuth's Seminumerical Algorithms. You should expect to spend 30 minutes to 2 hours on this quiz. You may use your text and any other resources to do this quiz, but if you do not know the answers well or are unable to discuss them in class, you will lose credit for the quiz.

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Please answer the following questions on this form (or on a paper copy of this form).

1. What are the prime factors of 264-1 and of 264+1?

2. Explain the differences among a two's complement computer, a one's complement computer and a signed magnitude computer. For each of them, assume binary numeric representations in your discussion.

3. Explain the differences among a ten's complement computer, a nine's complement computer and a signed magnitude computer. For each of them, assume decimal numeric representations in your discussion.

4. Explain the operation of a linear congruential random number generator. Give a specific example, explaining what it good and what is not so good about your choice.

5. Discuss the issues in finding the minimum value of a positive definite linear quadratic form.

6. Explain what answering question 5 has to do with testing random number generators.

7. Explain in detail a general method for finding a random number drawn from a continuous distribution with a given distribution function F(x).

8. Explain a good way to randomly select n records from a file containing N records, where N is very large.

9. What is a completely equidistributed sequence?

10. Explain the role of normalization in floating point arithmetic.

11. Discuss the handling of underflow in floating point arithmetic.

12. Discuss to role of the associative law in floating point arithmetic.

13. Discuss the role of software generated double precision arithmetic on a modern computer, not one from the 1960's.

<==== Do this AFTER you've answered all the questions

You probably DON'T want to do this ===>

Revised 19 September 2011