V22.0101 ......Homework Assignment 1 ...... Spring 2006
Binary Representation of Numbers

Assigned: WED, JAN 25.
First Version Due (by email to etutor): (Marateck) TUES, FEB 7, at midnight
Final Version Due (by email to etutor): 7 days after receiving comments from etutor

Decimal numbers from 0 through 255 can be represented in the binary number system using 8 bits. Here are some examples:

DecimalBinary
0 00000000
1 00000001
2 00000010
3 00000011
7 00000111
15 00001111
16 00010000
25 00011001
128 10000000
129 10000001
254 11111110
255 11111111
Thus, for example, the decimal number 25 is represented in binary as 00011001, meaning 0 times 128 plus 0 times 64 plus 0 times 32 plus 1 times 16 plus 1 times 8 plus 0 times 4 plus 0 times 2 plus 1 times 1. Notice that EACH BIT CORRESPONDS TO A POWER OF 2. Make sure you understand how this works before you go any further.

This assignment asks you to write a Java class called Binary. Every object of the class Binary will have a numerical value, which will be stored in the instance variable numVal. Another instance variable binStr will be used to store the binary string corresponding to numVal. In addition to its constructor, the class Binary will also have two methods that you must write. Here are the details.

• the public instance variable numVal (type int) (see the top of the template) is where the value of a number is stored by the class constructor (see below). Although it's tempting to think of this as the decimal representation of the number, since that is how System.out.println displays it, it is actually stored internally in a binary format that you cannot see.

• the public instance variable binStr (type String) is where the string of bits corresponding to the binary representation of the number is stored by one of the methods (see below).

• the constructor Binary (one parameter; notice that a constructor has the the same name as the class name and does not return a value) assigns a value to numVal. That's all the constructor has to do, using the int parameter that is passed to it. (See page 215 of the text.) However, the constructor should check to make sure the parameter value is between 0 and 255. If it is not, it should print an informative error message (using System.out.println) and store the number 0 instead.

• the method getBin (returns void, no parameters) should take the value that is in the instance variable numVal, generate the corresponding binary string and store it in the instance variable binStr. YOU MUST WRITE THIS METHOD BY YOURSELF. YOU MAY NOT CALL A METHOD FROM THE JAVA LIBRARY TO DO THIS JOB. YOU MAY NOT COPY FROM A CLASSMATE. HOWEVER, YOU MAY TALK TO YOUR CLASSMATES ABOUT HOW TO DO IT. The method should consist of a single for loop. This loop generates the 8 bits of the bit string, one at a time. There are two possible ways to do this. The easiest is to generate the bits from LEFT to RIGHT, by successively subtracting powers of 2 from numVal. Take the number 25 for example. If we subtract the biggest relevant power of 2, the number 128, from this, we get a negative answer so we know the first bit must be 0. The first power of 2 which is smaller than 25 is 16, so that tells us that the bit corresponding to that power (that's actually the fourth bit from the left) is 1. Once 16 is taken away from 25, we have 9 left. The next power of 2 is 8, which is less than 9, so the next bit (the fifth from the left) is also 1. Now we only have 1 left, so the sixth and seventh bits are 0, and the final eights bit is 1. You should not type all the powers of 2 into the program. You should start with 128, and then repeatedly divide this by 2 in the loop. YOU HAVE TO FIGURE OUT HOW TO EXPRESS THIS IDEA USING A FOR LOOP THAT WORKS AND IS WELL DOCUMENTED, EXPLAINING HOW IT WORKS ***WITH AN EXAMPLE***. Don't use any of the numbers in the table above for an example. Choose another number, say between 70 and 250 for your example. Don't use the same example as a classmate, if you can avoid it. (Of course, some people may choose the same example by accident -that's OK.) This explanation MUST APPEAR IN YOUR COMMENTS.

There's an alternative way to code this method, also using a for loop but generating the bits from RIGHT to LEFT, using repeated division. See p. 11 of the text. See the Powerpoint presentation at the last link for the homework http://cs.nyu.edu/courses/spring02/V22.0102-002/binary.ppt. Look at the slides up to the the ASCII table.

As each bit is generated, either left to right or right to left, you have to concatenate it to the current value of binStr. Start with the empty string.

• the method checkBin (returns Boolean, no parameters) should take the binary string in binStr and check to see if it correctly represents the number in numVal, essentially reversing the operation of getBin. This is easy, again using a loop: you need to extract the first bit of the string binStr, multiply it by 128, then add this to the second bit multiplied by 64, and so on. Again, don't type all the powers of 2 into the program: just start with 128 and repeatedly divide it by 2. Another variation is to first multiply the first bit by 2, then add the second bit and multiply all that by 2, and then add the third bit, and so on. Again, make sure you use a for loop and document it with COMMENTS. The method checkBin should return a Boolean value, indicating whether the result matches the number in numVal. To extract each bit, you need to use the String method charAt (see p. 256) to get the relevant char value and you can then test this against the char values '0' and '1' to complete the job. As with getBin, you must give DETAILED COMMENTS with an EXAMPLE (use the same example you used for your comments in getBin).
The template also has a class called TestBinary with just one method, the main one. This goes in the same file as class Binary, but at the top. Because TestBinary contains the main method, the Java file name MUST be called TestBinary.java. TestBinary is public but Binary cannot be public because Java permits only one public method per file. The main method of TestBinary is supposed to test the methods in class Binary. You should run TestBinary on lots of examples to make sure everything is working correctly. You can "hard-wire" the example numbers into the main method, or you can read them from the the keyboard using the JOptionPane class described in the text book (page 855). the simplest form to use for assigning input to a string, let's say number is String number = JOptionPane.showInputDialog("Type your decimal number");. If you use this approach, remember to end the main method with System.exit(0) otherwise the program will hang. Notice that you cannot access the instance variables numVal and binStr outside the Binary class because their access is private.

After your program runs properly, alter it slightly so that it can read the data from the command line. If you have a mac, the terminal program gives you the command line. If you have a PC, see http://www.computerhope.com/issues/ch000549.htm (the link is on the web page under the assignment) for how to include the java and javac programs in your path. However, the easiest way is to place your program in the Bin directory of the jdk directory. Hand this version into your etutor. If you can't get this version to work, 0.2 points will be deducted from a possible high of 4.0 points.

Please get started on the assignment immediately, and contact your etutor as soon as possible with any questions. Don't expect a response the day before the due date. Late homeworks will be accepted up to 7 days late, but they will be penalized 25%.