CS074-Digital World

Review

Summary of Course Contents

Units of Information

Understand the terms bit, byte, kilobyte, megabyte, gigabyte so that you are able to translate easily between them.
Understand that there are 2ⁿ different sequence of n bits, and all that this entails.

Binary Encoding of Numbers

Understand how positional number systems work and how to convert between representations at different bases, and how to do arithmetic at different bases.
Understand, in particular, representation at bases two (binary), ten (decimal), and sixteen (hex); as well as conversion between these bases.

Binary Encoding of Text

Understand the fundamentals of ASCII. You don't need to memorize the encodings of any characters, but you should understand that each character is encoded by a single byte, that the digit characters '0' - '9' have consecutive codes, likewise the upper-case letters 'A'-'Z' and the lower-case letters 'a'-''z'.
In particular, understand that a character string like "193" is encoded by three bytes, and that the binary representation of the number 193 as an integer is something entirely different.
Be at least aware that there are other systems, like Unicode, which uses two bytes to encode a character.

Binary Encoding of Images

Understand the most straightforward way of encoding images: 24-bit bitmapped color images, in which each pixel is represented by a three-byte RGB encoding of the color.
Be able to solve simple problems in which some transformation of the bytes of the representation results in a desired change in the image.
Be aware that there are other possibilities, especially compressed formats like GIF and JPEG, although you don't need to know the details of how these formats work.

Binary Encoding of Sound

Understand the notion of sampling, and the structure of .wav files, in which every sample is represented by a number (in our examples in class, a single byte).
Be able to solve simple problems in which some transformation of the bytes of the representation results in a desired change in the sound.
Be aware that there are other possibilities, especially compressed formats like MP3, although you don't need to know the details of how these formats work.

Compression Basics

Understand the distinction between lossless and lossy compression, and when one or the other is appropriate.
Understand what "compression ratio" is.
Understand the principles of lossless compression---redundancy in information, and using methods like Huffman coding to reduce redundancy.

Python Programming

Variables, assignment, simple arithmetic expressions.
Basic data types: integer, floating point, and string. Different meanings for + operator when applied to strings or numbers. Different meanings for / operator when applied to integers or floating point numbers.
Arguments and return values in functions.
for statement to loop over elements in a list or a string.
relational operators (<,>,<=,>=,==,!=), logical operators (and, or, not), and if, elif, else statements.
random number generation
strings
lists
Applications: Manipulating image files.
Applications: Drawing on images.
Applications: Getting information from the Web.

Internet Basics

IP addresses
Protocols for different internet services. You don't need to know any details about protocols like SMTP and HTTP---just that there is some standard format for the exchange of messages in each of these.
HTML--again, you don't have to know any HTML details, just to be aware that Web pages are encoded as text files written in HTML.

Problems

1. 'Textese', or 'SMS language' refers to the style in which text messages are written. Since people firing off text messages tend to ignore capitalization and punctuation, and since line breaks are handled automatically, textese in effect uses a character set consisting of just 26 letters, the 10 digits, and a space. Suppose we want to devise a binary encoding of this character set.
(a) What is the least number of bits required to encode each character, assuming that we use the same number of bits for each character?
(b) In the earliest days of SMS, text messages were limited to 160 characters. Assuming you use the encoding of part (a), what is the maximum number of bytes in such a text message?

2. Write in both decimal and hex the number whose binary representation is 1101011.

3. Write two hundred thirty three in both binary and hex.

4. Describe the steps you would have to perform in the Binary Editor to convert a color bitmap image into a grayscale negative. (Pictured below.)

5. The steps you carried out in Problem 4 involve a certain operation, or sequence of operations, applied to the bytes of a file. Suppose you applied exactly the same operations to the audio samples in a .wav file. What would be the effect on the sound?

6. This problem describes a data compression technique used to compress black-and-white images, in which each pixel is either black or white, and thus represented by a single bit. It is well suited for things like fax messages that consist of text and simple line drawings.

(a) Just to get things started off, before we describe the compression technique, how many bytes are required to encode a 400 pixel x 400 pixel image when each pixel is represented by a single bit.

The data compression method looks at each row of the image. Suppose a row consist of 280 white pixels, followed by 3 black pixels, followed by 74 white pixels, then 2 black pixels, then 41 white pixels. This row will be encoded as the sequence of numbers 280,2,74,2,41. We will use two bytes for each number (why?) Thus the number of bytes used to encode each row is twice the number of alternations between black and white that you find as you scan along the row. This compression method is called run-length encoding. The full encoding of the image will contain the encoding of each row, together with two bytes telling the number of pixels in each row.

(b) Is this a lossless or lossy compression method? Explain.

(c) Suppose that, on average, each row is encoded by five numbers, as in our example above. What compression ratio is achieved in encoding a 400x400 pixel image in this fashion?

(d) Which of these two images will be compressed more by this method: A brief handwritten note (about 50 words) or a typewritten page of text (about 200 words)? Explain.

7. What are the values of the variables x and y after the following Python statements are executed?

    x=7/2*3.5
    y="boston"+str(x)

8. Write a python program that draws a house, but paints it in randomly chosen colors. Thus you should get a different color scheme each time you run the program. Here's a much trickier question: Then try to rewrite the program in a fashion so that the difference between the largest and smallest components of the color is at least 150---this should give you a highly saturated color.

9. Write a python program that opens an image file and displays a grayscale negative of the image---essentially question 4 above, but now you have to write it in python.

10. (a) The following python function convert is meant to take an integer argument in the range 0 to 255 and returns a string of length 2. What string is returned when the argument is 97? What useful thing is this function doing in general? What happens when you pass this function an argument outside the prescribed range (like -2 or 256)?

    def convert(num):
    code="0123456789ABCDEF"
    result=code[num/16]+code[num%16]
    return result

(b) Write a python function that prompts the user to enter an integer at the keyboard and then prints the value returned when this integer is passed to convert as an argument. In other words, your function should call convert. Your function should also check to see if the integer is in the appropriate range, and print an error message if it is not. You can use the built-in JES function requestInteger: this will check that the input really is an integer.

11. Write a python function that does the reverse of the function convert in 8(a): This should take a string of length 2 as an argument and return the corresponding integer. (To do this, you really need to understand the useful thing that convert does.) There are several approaches to this problem. It can be useful to know (a) you can compare characters using < (for instance 'a'<'d' is true); (b) the ord function gives the ASCII code of a character; (c) the chr function reverses the ord function, i.e., it returns the character whose ASCII code is the argument.