Lab 5 In-Class: Exploring Data Representation & Conditional (if) Statements

Log onto the Linux system and create a lab5 subdirectory of your cpsc120/labs directory for today's work. As usual, you will need to have three windows open: an xterm, emacs, and Netscape.

A Base Conversion Program

In class we learned an algorithm for converting a base 10 number to another base by repeatedly dividing by the base. Each time a division is performed the remainder and quotient are saved. At each step, the number used in the division is the quotient from the preceding step. The algorithm stops when the quotient is 0. For example to convert the base 10 number 1878 to base 8 you would do the following:
                            Quotient      Remainder
    1878 divided by 8 -->     234             6
     234 divided by 8 -->      29             2
      29 divided by 8 -->       3             5
       3 divided by 8 -->       0             3

The number in the new base is the sequence of remainders in reverse order (the last one computed goes first; the first one goes last). In this example, the base 8 answer is 3526 (that is 187810 = 35268). In this exercise you will use this algorithm to write a program that converts a base 10 number to a 4-digit number in another base (you don't know enough programming yet to be able to convert any size number). The base 10 number and the new base (2 - 9) will be input to the program. The start of the program is in the file Open the file in Netscape, save it to your lab5 subdirectory, then open it in emacs. Modify the program one step at a time as follows:
  1. The program will only work correctly for base 10 numbers that fit in 4 digits in the new base. We know that in base 2 the maximum unsigned integer that will fit in 4 bits is 11112 which equals 15 in base 10 (or 24 - 1). In base 8, the maximum number is 77778 which equals 4095 in base 10 (or 84 - 1). In general, the maximum base 10 number that fits in 4 base b digits is b4 - 1. Add an assignment statement to the program to compute this value for the base that is input and assign it to the variable maxNumber. Add a statement that prints out the result (appropriately labeled). Compile and run the program to make sure it is correct so far.
  2. Now it is time to add the code to do the conversion. The comments below guide you through the calculations -- replace them with the appropriate Java statements. Note that you will need to declare a new variable to hold the quotient.
        // First compute place0 -- the units place.  Remember this comes
        // from the first division so it is the remainder when the
        // base 10 number is divided by the base (HINT %).
        // Then compute the quotient (integer division / will do it!) and
        // store the result into the quotient variable.
        // Now compute place1 -- this is the remainder when the quotient
        // from the preceding step is divided by the base.  
        // Then compute the new quotient and store the result into
        // the quotient variable.
        // Repeat the idea from above to compute place2 and the next quotient
        // Repeat again to compute place3
  3. So far the program does not print out the answer. Recall that the answer is the sequence of remainders written in reverse order -- note that this requires concatenating the four digits that have been computed. Since they are each integers, if we just add them the computer will perform arithmetic instead of concatenation. Instead, we can use a variable of type String and then use the + operator to do string concatenation. (Remember that if either parameter to + is a string, it does concatenation instead of addition.) Near the top of the program a variable named baseBNum has been declared as an object of type String and initialized to an empty string. Add statements to the program to concatenate the digits in the new base to baseBNum and then print the answer. Compile and run your program. Test it using the following values: Enter 2 for the base and 13 for the base 10 number -- the program should print 1101 as the base 2 value; enter 8 for the base and 1878 for the number -- the program should print 3526 for the base 8 value; enter 3 for the base and 50 for the number -- the program should print 1212.
  4. Don't print your program yet! You are going to add something to it later.

Color Codes

The basic scheme for representing a picture in a computer is to break the picture down into small elements called pixels and then represent the color of each pixel by a numeric code (this idea is discussed in section 1.5 of the text). In most computer languages, including Java, the color is specified by three numbers -- one representing the amount of red in the color, another the amount of green, and the third the amount of blue. These numbers are referred to as the RGB value of the color. In Java, each of the three primary colors is represented by an 8-bit code. Hence, the possible base 10 values for each have a range of 0-255. Zero means none of that color while 255 means the maximum amount of the color. Pure red is represented by 255 for red, 0 for green, and 0 for blue, while magenta is a mix of red and blue (255 for red, 0 for green, and 255 for blue). In Java you can create your own colors. So far in the graphics programs we have written we have used the pre-defined colors, such as, from the Color class. However, we may also create our own Color object and use it in a graphics program. One way to create a Color object is to declare a variable of type Color and instantiate it using the constructor that requires three integer parameters -- the first representing the amount of red, the second the amount of green, and the third the amount of blue in the color. For example, the following declares the Color object myColor and instantiates it to a color with code 255 for red, 0 for green, and 255 for blue.

       Color myColor = new Color(255, 0, 255);

The statement page.setColor(myColor) then will set the foreground color for the page to be the color defined by the myColor object. The file contains an applet that defines myColor to be a Color object with color code (200, 100, 255) - a shade of purple. Save the program and its associated HTML file Colors.html to your lab5 directory, compile and run it using the appletviewer. Now make the following modifications:
  1. Change the constructor so the color code is (0,0,0) --- absence of color. What color should this be? Run the program to check.
  2. Try a few other combinations of color codes to see what you get. Page 793 of the text shows you the codes for the pre-defined colors in the Color class.
  3. Now we will modify the program to generate random colors. Notice on page 793 of the text that there is a constructor for the Color class that takes a single integer as an argument. The first 8 bits of this integer are ignored while the last 24 bits define the color -- 8 bits for red, 8 for green, and the last 8 bits for blue. Hence, the bit pattern
    should represent pure green. Its base 10 value is 65280. Change the declaration of the myColor object to
            Color myColor = new Color (65280);
    Compile and run the program. Do you see green?
  4. Now add the following statements to the program: Compile and run the program -- reload the program several times so you can see the different random colors generated.
  5. The Color class has methods that return the individual color codes (for red, green, and blue) for a Color object. For example,
            redCode = myColor.getRed();
    returns the code for the red component of the myColor object (redCode should be a variable of type int). The methods that return the green and blue components are getGreen and getBlue, respectively. Add statements to the program, similar to the above, to get the three color codes (you need to declare some variables). Then add statements such as
            page.drawString("Red: " + redCode, ____ , ____ );
    to label the rectangle with the three color codes (fill in the blanks with appropriate coordinates so each string is drawn inside the rectangle -- you also need to set the drawing color to something such as black so the strings will show up). Compile and run the program to make sure it works. Reload several times to see the different colors and their corresponding codes displayed.
  6. Print the final version of your applet.

A Program Using If Statements (Conditionals)

A conditional statement (also called a selection statement) in a programming language is one that allows a choice as to which statement is executed next. That choice is based on some condition -- a boolean expression that is either true or false. In Java (and most other programming languages) two of the conditional statements are if and if ... else... . If and if ... else... statements are discussed in Section 3.2 of the text. An if statement is used when you want to do something when some condition is true but do nothing otherwise. Some examples are:
       if (grade >= 90)
         System.out.println ("Congrats!  You made an A!");
In this example the condition is grade >= 90 (grade would be a variable given a value earlier in the program). If it is true (if the value of the variable grade is greater than or equal to 90 when this statement is executed) the congratulation statement would be printed; otherwise it will not be printed.
       if (numStudents != 0)
          testAverage = sumOfGrades / numStudents;
In this example, the condition is numStudents != 0. != is the "not equal" operator. If the value of the variable numStudents is not equal to 0 when the condition is evaluated, the assignment statement will be evaluated.

An if ... else ... statement is used when you want to do one thing when a condition is true but something else when it is false. Some examples are

        toss = Math.abs (generator.nextInt()) % 2;
        if (toss == 0)
           System.out.println ("Tails");
           System.out.println ("Heads");
In this example the condition is toss == 0, where == is the "equal" operator. (Remember a single = mark is the assignment operator.)
        if (numStudents > 0)
           testAverage = sumOfGrades / numStudents;
           System.out.println ("You must have at least one student!!");

The file contains a program to compute a customer's water and sewer bill. The charge for water is based on consumption -- a customer who uses no more than 7500 gallons in a month pays $0.002 per gallon but a customer who uses more pays $0.002 per gallon for the first 7500 gallons plus $0.0035 per gallon for each gallon over 7500. Note that the charge depends on a condition -- whether or not the amount of water used is over 7500 gallons. Hence an if is needed to compute the charge for the water. Do the following:

  1. Save the file to your directory and open it in emacs.
  2. Study the code and find the if... else... that computes the charge for the water -- there are two different formulas used for the calculation depending on whether numGals is less than or equal to CUTOFF (7500) or not. Also notice near the bottom of the program an if that prints a message for customers who use less than half of 7500.
  3. Run the program several times. Enter numbers greater than 7500 (such as 10000), numbers between 7500 and half of 7500 (such as 6000), and numbers less than half of 7500 (such as 3000).
  4. Suppose the charge for sewer services is also based on water usage. A person who uses less than 7500 gallons of water pays a flat rate of $7.50 for sewer but a person who uses more pays $0.001 per gallon. Add an if ... else... to the program to compute the sewer charge. Update other parts of the program to take this into account -- update the calculation of the total bill and add a statement to print the sewer charge in the bill.
  5. Suppose senior citizens get a break on the utility tax. The tax rate for senior citizens is 8.5% but it is 12% for all others. Add statements to the program to compute the tax. This requires that you find out if the customer is a senior citizen! Use a variable of type char for this. You need to do the following:
    1. Add a prompt that asks the user to answer the question "Are you a senior citizen?" by entering a y or n. Use the Keyboard class to read in the answer (as a char not a String); store the answer in the variable senior.
    2. Write an if to compute the utility tax.
    3. Add the utility tax to the total bill.
    4. Print the utility tax as part of the bill.
  6. Add an if statement that prints a warning to customers who use more than 3 times the cut off (7500) gallons. Warn them that they are subject to a $500 fine if their excessive water use continues (just print a message -- don't add the fine to their bill)!
  7. Be sure your program works correctly, then print it.

Adding an if to the Base Conversion Program

Get your base conversion program back (note -- instead of re-opening it, look under buffers on the emacs menu bar, then click on Remember that this program only computes 4 digits in the new base so if the user enters a number that is too large to fit in 4 digits the answer produced by the program is incorrect (it is incomplete -- it only gives the rightmost 4 digits). Unfortunately a lot of people believe the computer so we need to be sure the computer doesn't print out incorrect information. Replace the statement that prints the answer with an if ... else ... If the number is too large to fit in 4 digits in the new base print a message saying so (remember you calculated the maximum number that will fit); otherwise, print the answer. To test the program, use the following input: 4 for the base and 375 for the base 10 number (the program should say 375 is too big to fit in a 4-digit base 4 number); 7 for the base and 5341 for the number (again, too big); 7 for the base and 537 for the base 10 number (the program should print 1365).

Print a copy of your program.

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