Espresso: A Concentrated Introduction to Java

Laboratory: Binary Representation of Integers

Summary: In this laboratory, you will explore the binary representation of integers in Java.

Corresponding Reading:

Class Documentation::



Exercise 0: Preparation

a. Review Binary Representation of Integers in Java.

b. Create a new project for this lab, called Binary, and package within that project, called username.binary. Note that you should use your own username in place of username.

mkdir /home/username/CSC152/Binary
mkdir /home/username/CSC152/Binary/username/
mkdir /home/username/CSC152/Binary/username/numbers

c. Start Eclipse and load this project.

Exercise 1: Confirming Prior Results

In the lab on numbers, you discovered that when you added a small value to the largest int (Integer.MAX_VALUE), you got a negative number and when you subtracted a small value from the smallest int (Integer.MIN_VALUE), you got a positive number.

The reading on binary representation suggests why: Java limits the number of bits with which it represents numbers and uses two's complement notation.

Redo the experiment, printing out the binary representation of each value. That is, print the binary representation of Integer.MAX_VALUE, the small integer you added, the sum of those two values, Integer.MIN_VALUE, the small integer you subtracted, and the difference of those two values.

Recall that you can use Integer.toBinaryString(i) to extract the binary representation of an int.

Exercise 2: From Decimal to Binary

Write a class, DecimalToBinary, that prompts the user for two integers in base-ten form, prints their representation in binary, prints their sum in binary, and prints their difference in binary.

For example,

Enter an integer: 10
Enter another integer: -3
1010 + 11111111111111111111111111111101 = 111
1010 - 11111111111111111111111111111101 = 1101

Note that you will need to use Integer.parseInt to convert the input strings to int values.

Exercise 3: Adding Leading Spaces

One disadvantage of the prior output is that it doesn't make it immediately clear how the two added values line up. Write a new version of the class that does vertical addition, giving output something like the following:

Enter an integer: 10
Enter another integer: -3

+ 11111111111111111111111111111101 

- 11111111111111111111111111111101 

Note that you can add the leading spaces by a clever combination of append, substring, and Integer.numberOfLeadingZeros(i).

Exercise 4: Exploring Bitwise Operations

Write a program, BitOps, that allows you to explore the various bitwise operations (&, |, ^, >>, <<).

For example, here's part of the output.

Enter an integer: 10
Enter another integer: 2

  00000000000000000000000000001010 (10)
& 00000000000000000000000000000011 (3)
  00000000000000000000000000000010 (2)

10 << 3 = 80
  00000000000000000000000000001010 << 3 
  => 00000000000000000000000001010000


Tuesday, 7 February 2006 [Samuel A. Rebelsky]

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Samuel A. Rebelsky