## Math 110-01, Spring 2008 Assignment 8

Reminder: There is a test next Friday, April 4.

This assignment is due in class on Wednesday, April 2.

### Exercise 1

Pick one of the topics from the list of possible topics for the final project, and do a little research into it. List two sources that you have consulted; they can be URLs for sources on the Web. Write a short paragraph about the topic, describing what you find. You want to give some idea of what might be covered in a complete project on the topic.

### Exercise 2

Pick a second possible for your final project. It can be either another one of the topics from the list of possible topics, or it can be something that you come up with on your own. Do the same thing for the second topic as you did for the first one in Exercise 1. That is, list two sources and write a short paragraph about the topic.

### Exercise 3

Here are a few problems to give you some more practice on different number bases:

1. Convert the base-10 number 267 into base-8. (That is, find the base-8 representation of the number that is represented in base-10 by the symbol "267".)
2. Consider a base-12 system in which the numbers from zero to eleven are represented as 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B. Convert the base-12 number 7B5 into base-10.
3. Beings on the planet Trantor use a base-3 number system in which the numbers that we represent as 0, 1, and 2 are represented by the symbols #, @, and %. How would someone on Trantor represent the number that is written in base-10 as 31?
4. Imagine a base-26 number system in which letters A, B, C,..., Z represent the 26 basic digits. (A=0, B=1, C=2, ..., Z=25). What base-10 number is represented by the base-26 number "CAT"?

### Exercise 4

And here are few modular arithmetic problems. Compute the value of each of the following expressions:

1. 100 mod 7
2. -23 mod 100
3. 2 + 2 mod 3
4. 17 + 28 mod 32
5. 13 * 10 mod 20

### Exercise 5

Encode the following plaintext using a Caesar Cipher with shift amount equal to 7:

```      COMMONSENSEISNOTVERYCOMMON
```

### Exercise 6

The following ciphertext was encoded using as a one-time pad the characters on page 171 of the book ZERO: The Biography of a Dangerous Idea:

```      SOEGGGSAYRXUMSZBLTQGTHZ
```

Decode this message. The message is a question. Encode your answer to the question using the characters on page 98 of ZERO as a one-time pad.