Posted: March 3, 2005
Due: March 20, 2005

DO NOT IMMEDIATELY ATTEMPT TO PRINT THIS OUT. YOU WILL SWAMP THE PRINTERS AND WASTE PRECIOUS LAB TIME. YOU MAY OPEN MORE THAN ONE WINDOW! KEEP THIS PAGE OPEN WHILE YOU WORK.

Introduction

Objectives of the Lab:

• the binary number system, and how addition works
• how to use boolean variables
• simple if/then statement and contrast with returning a boolean
• how inheritance can be used to extend a class, and therefore re-use its methods

• using function composition to express a solution
• passing arguments
• using more than two classes
• reading and modifying existing code

Background (READ CAREFULLY!!!!):

1278 represents the number 1*10³ + 2*10² + 7*10¹ +8*10⁰

In octal system (base = 8, digits : 0,1,2,3,4,5,6,7) the number 1274 represent the value 1*8³+2*8²+7*8¹+4*8⁰= ...

Digital computers use two digits to count (0 and 1). When we reach "2" we carry a 1 to the next column. Numbers greater than 1 can be represented by using a notation that makes use of the powers of 2. For example:

10010 represents the number 1*2⁴ + 0*2³ + 0*2² + 1*2¹ +0*2⁰
This is equivalent to 2⁴ +2¹ which equals 16 + 2, which equals 18.

Addition in binary is performed using the following principles: 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, and 1+ 1 = 10 (where we carry the 1).

For example:

 

1001

+0111

10000

Binary addition consists of three input and two output values. The input values are the carry in (which is 0 for the right most column), and the two digits for the column currently being added. The output values are the carry out and the sum. The carry out from one column is the carry in for the column to its left. The addition above can by expressed as follows:
 

	carry in	A's digit	B's digit	carry out	sum
Step1	0	1	1	1	0
Step 2	1	0	1	1	0
Step 3	1	0	1	1	0
Step 4	1	1	0	1	0
Step 5	1	1	1	1	1

The Task:

Write Boolean expressions for the CarryOut and the Sum.

CarryOut = (! CarryIn && A && B ) ||

                   (CarryIn && !A && B ) ||

                   (CarryIn && A && !B ) ||

                   (CarryIn && A && B)

Step 2: Your text shows you how to write Boolean expressions in Java. By way of review: the "!" operator negates a Boolean value, the "&&" operator "ands" two Boolean values and the "| |" operator "ors" two values. Express your solutions to step 1 as Java. Examine the program FullAdder.java and fill in the missing pieces. Look for the comments that say "FIX THIS." You can copy the code from ~mmmartin/www/CMSC220Labs/Labs/Lab4/AdderCode. Note that there is a function XOR defined in Adder that you might find useful.

You will need to write a worker class that tests all eight cases given in the table above. For example, use the KeyIn method readBoolean() to request Boolean values (look up readBoolean in the index of your book). You will also need to write an application class to start up your worker class. If you get stuck in the logic, you may use the Adder.class method in the AdderCode structure for the next step.

Step 3: A cascading adder is one that hooks the carry out from one column to the carry in of another. Examine the class AdderCode/Arithmetic.java and try running the ArithApp class. The Arithmetic.java file contains comments that say "QUESTION". Answer them directly in the code, then save the file under the name "Answers.java".

Step 4: Make a copy of the original Arithmetic.java code and then modify the code as specified in the comment at the top labeled "MODIFY INSTRUCTIONS". If you keep the Arithmetic.java name for this file, then you can re-use the ArithApp class for testing.

Requirements:

In this lab you are required to produce a lab report and to arrange for a demo of your solutions. Do NOT!!! include code in your lab report.

Demo:

The code you write should include:

• A clearly defined header identifying
  • the programmers
  • the course
  • the date
  • and the lab assignment
• Clearly commented code

Lab report:

• a cover page identifying the programmers
• for each step include
  • the statement of the task (don't just cut and paste the instructions, summarize them.)
  • an analysis section that shows how you designed the implementation(s) (you do not need to belabor this, simply show that some work went into design and analysis BEFORE implementation)
  • clearly state where the code may be accessed e.g. ~studentName/Lab4/Step1
  • include any discussion relevant to the questions that appear in the steps above.

• a general summary stating
  • what you found easy about this lab
  • what you found difficult about this lab
  • if you worked as a team, who did what, and whether collaboration helped or hindered your work

Hints and Other Advice:

ASK!!!!!!! questions, in class, in lab, during office hours and especially via the class newsgroup. Please do not phone.

GET HELP FROM ANY ONE AND EVERYONE. If there is something that is not clear to you ASK!!!!