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

What is your age in seconds?

• years, months, days, and seconds should be integers
• declare a conversion constant SECONDS_PER_DAY and in the initialization have the computer do the arithmetic (in other words you shouldn't get out your calculator and figure out how many seconds are in a day -- write the expression so the computer has to do the work)
• define other constants and/or variables as needed
• assume there are 30 days in a month and 365 days in a year

• Run your program to see how many seconds has a person who is 68 years, 6 months, and 12 days old lived.

You should have gotten a strange answer to the last question! Why did your program produce such an answer? Hint: Java uses a 32-bit two's complement representation for type int. Given this, compute the largest int value that Java can represent -- you'll have to remember the formula for the largest value that can be stored in an N-bit two's complement number, then get out your calculator (or use the calculator under Accessories) to compute it. ***Note both the formula and the value itself, and write them on the program (to turn in) when you print it out.*** Now look at the other ages in seconds you have computed, e.g., 21 years. 68 years is a little over triple that value; is this consistent with your strange answer? (No need to write this answer.)

Fix your problem as follows:

• Change the type of ONE (and only one) variable from int to long, which is a 64-bit integer representation. Your program should still work exclusively with integers, not floating point numbers.
• The above change will not completely solve the problem (run your program and see). You need to make sure the expression is computed using the larger data type - a carefully placed cast operator should do the trick!

Test the program again and make sure it works. A person who has lived 68 years, 6 months, and 12 days is 2,161,036,800 seconds old.

A Base Conversion Program

                            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

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.

       // 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!) -
       // declare a new variable for the quotient
   
   
   
   
       // Now compute place1 -- this is the remainder when the quotient
       // from the preceding step is divided by the base.  
       // Then compute the new quotient
   
   
   
   
       // 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 use the + operator the computer will perform arithmetic instead of concatenation. But remember that if either operand to + is a string it will do concatenation, and that in the case of multiple + operations they are performed from left to right. So if you start by concatenating "" (the empty string), it will force the rest of the values to convert to strings -- essentially you are concatenating the values of the four place variables to the empty string. You can store the result in a String variable or just print it directly.

   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

           Color (int r, int g, int b)

The file Colors.java contains an applet that you will use to experiment with your own colors (and random colors). Save the program and its associated HTML file Colors.html to your lab5 directory, then do the following:

1. Add a statement (as directed by the comment in the program) that declares myColor to be a Color object and instantiates it to be the color with color code 200 for red, 100 for green, and 255 for blue - this gives a shade of purple. Compile and run the applet using the appletviewer.
2. Change the constructor so the color code is (0,0,0) --- absence of color. What color should this be? Run the program to check.
3. 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.
4. 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

           00000000000000001111111100000000
   

   should represent pure green. Its base 10 value is 65280. Change the declaration of the myColor object to instantiate myColor to be an object with color represented by the single integer 65280. Compile and run the program. Do you see green?
5. Now add the following statements to the program:
   • declare generator to be an object of type Random (the import statement is already there);
   • declare colorCode to be a variable of type int;
   • assign colorCode a random integer value (use the nextInt() method);
   • replace the number 65280 in the Color constructor above with the variable colorCode
   Compile and run the program -- reload the program several times so you can see the different random colors generated.
6. The Color class has methods that return the individual color codes (for red, green, and blue) for a Color object. For example, the getRed() method returns the code for the red component of the myColor object. The methods that return the green and blue components are getGreen() and getBlue(), respectively. Add statements to the program to declare three integer variables redCode, greenCode, and blueCode and to get the three color codes and assign them to the appropriate 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.

A Program Using If Statements (Conditionals)

       if (grade >= 90)
         System.out.println ("Congrats!  You made an A!");

       if (numStudents != 0)
          testAverage = sumOfGrades / numStudents;

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");
        else
           System.out.println ("Heads");

        if (numStudents > 0)
           testAverage = sumOfGrades / numStudents;
        else
           System.out.println ("You must have at least one student!!");

The file WaterBill.java 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 $0.001 for sewer but a person who uses more pays $7.50 for the first 7500 gallons plus $0.003 per gallon for each gallon over 7500 (so, for example, a person who used 8500 gallons would pay $7.50 + $3.00 = $10.50). 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 (note: the tax is on the total bill).
   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

Print a copy of your program.

Hand In

• The four programs (your age program, BaseConvert.java, Colors.java, and WaterBill.java).
• Tar your directory and email it to your instructor at roanoke.edu with the subject cpsc120 lab5.