The Digital World-Homework 1

Posted February 2

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You Don't have to Hand These In

As explained in the syllabus, the homework problems--as opposed to the lab assignments--are not collected or graded.  But you should definitely try to do them before you look at the posted solutions, as they are typical of the kinds of problems you will see on quizzes and tests.

How to Cheat on this Homework

Well, if the problems aren't collected or graded, I guess there's no such thing as really cheating.  But you can check your answers to these questions using a calculator that's built into Google.  You denote values in binary by preceding them with "0b", and values in hex by preceding them with "0x".  Type

"0b1101001 in decimal"

and Google will do the base conversion for you.  If you type

"0x3ae2 * 0x5a4f ="

it will display the product in hex.  (I find it amusing that you can send these arithmetic problems over the Internet and have a computer in California solve them for you!)

As I say, that's fine for checking your results, but you really do need to know how to figure these answers out on your own.  So take the time to learn the algorithms and apply what you learned to these examples.

Exercises

1. Write, in ordinary decimal notation, the integer whose binary representation is 11011001.

2. Write the binary representation of one hundred sixty-nine

3. Write the bit pattern of problem 2 in hexadecimal notation.

4. Add 100101 and 11101011 in binary.  Don't do this by converting to decimal, adding, and then converting back to binary, do the entire problem in binary. Now multiply 11010 and 10111 in binary.

5. What are the three numbers displayed in the Maya manuscript in the Lecture Notes "Representing Numbers"?  (The base is 20.  Each digit consists of either the eye-shaped thing, which is zero, or between zero and three parallel lines and between 0 and 4 dots.  Each dot represents 1 and each line represents 5, so each digit value is between 0 and 19.  The most significant digit is at the top.)

6. How many bytes are in the ASCII representation of a  typical novel?  For a typical novel, you can just pick anything off your bookshelf, and make a reasonable estimate.  Explain how you made the estimate.  A CD  has a storage capacity of 650MB.  Approximately how many such novels will fit on a single CD, using the ASCII encoding of one byte per character?

7. Practically no one uses dialup anymore, because they're so slow. The built-in dialup modems on many computers receive and transmit at 56 kilobits per second (if you're lucky).  A kilobit is really one thousand bits, I think. How long would it take to download the entire contents of an audio CD using dialup?

8. In the directory of numbers in my cell phone, there is a number labeled.

and another labeled

This directory is presumably in alphabetical order, but "HOWARD WORK" comes before "Home". Why is that?