CS 570: Homework Assignment 1

CS 570: Homework Assignment 1

1 Assignment Policies
Collaboration Policy. Homework will be done individually: each student must hand in
their own answers. It is acceptable for students to collaborate in understanding the material
but not in solving the problems or programming. Use of the Internet is allowed, but should
not include searching for existing solutions.
Under absolutely no circumstances code can be exchanged between students.
Excerpts of code presented in class can be used.
Your code must include a comment with your name.
2 Assignment
Define a class BinaryNumber that represents binary numbers and a few simple operations on
them, as indicated below. An example of a binary number is
1011
Its length is 4. Note that its leftmost digit is the least significant one: it represents the
decimal number 1 ∗ 2
0 + 0 ∗ 2
1 + 1 ∗ 2
2 + 1 ∗ 2
3 = 13. This is called little-endian format. You
may use big-endian if you prefer; in that case you must state so at the beginning of your
code as part of the comment.
This assignment requests that a number of operations be supported. They are divided
into two groups. The first is a set of basic operations, the second is slightly more challenging
and addresses addition of binary numbers.
2.1 Basic operations
The following operations should be supported:
• A constructor BinaryNumber(int length) for creating a binary number of length length
and consisting only of zeros.
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• A constructor BinaryNumber(String str) for creating a binary number given a string. For
example, given the string "1011", the corresponding binary number should be created.
For this exercise you will have to use some standard String operations. These are listed
in the “Hints” section below.
• An operation int getLength() for determining the length of a binary number.
• An operation int getDigit(int index) for obtaining a digit of a binary number given an
index. The starting index is 0. If the index is out of bounds, then a message should
be printed on the screen indicating this fact.
• An operation int toDecimal() for transforming a binary number to its decimal notation
(cf. the example given above).
• An operation void shiftR(int amount) for shifting all digits in a binary number any
number of places to the right, as indicated by a parameter amountToShift. The new
digit should be 0. For example, the result of shifting “1011” 3 places to the right
should yield “0001011”.
2.2 Addition of Binary Numbers
Here is an example of how two binary numbers of the same length are added1
.
1 1 1 1 (carried digits)
1 0 1 1 0
+ 1 1 1 0 0
= 0 0 1 0 1 = 20
Note that it is possible for the addition of two numbers to yield a result which has a
larger length than the summands. In that case, this should be flagged by an appropriate
boolean data field. Here is such an example.
1 1 1 1 1 (carried digits)
1 0 1 1 0
+ 1 1 1 0 1
= 0 0 1 0 0 1 = 36
This data field should be added to the data fields of the class BinaryNumber.
Implement the following operations:
• void add(BinaryNumber aBinaryNumber) for adding two binary numbers, one is the binary
number that receives the message and the other is given as a parameter. If the lengths
of the binary numbers do not coincide, then a message should be printed on the screen
indicating this fact. Otherwise, it modifies the receiving binary number with the result
of the addition.
• An operation clearOverflow() that clears the overflow flag.
• An operation String toString() for transforming a binary number to a String. If the
number is the result of an overflow, the string “Overflow” should be returned.
1Source: https://en.wikipedia.org/wiki/Binary_number
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2.3 Hints
• For the BinaryNumber(String str) constructor, the following operations might come in
handy:
– char java.lang.String.charAt(int index), which returns the char value at the specified index. An index ranges from 0 to length() - 1. The first char value of the
sequence is at index 0, the next at index 1, and so on, as for array indexing.
– int java.lang.Character.getNumericValue(char ch), which returns the int value that
the specified Unicode character represents.
• For the shiftR(int amount) operation, it might be useful to define an auxiliary private
method reallocate, that makes room for a new digit. This operation would in turn use
int[] java.util.Arrays.copyOf(int[] original, int newLength), which copies the specified
array, truncating or padding with zeros (if necessary) so the copy has the specified
length.
3 Submission instructions
Submit a single file named BinaryNumber.java through Canvas. No report is required.
Your grade will be determined as follows:
• You will get 0 if your code does not compile.
• The code must implement the following UML diagram precisely.
• We will try to feed erroneous and inconsistent inputs to all methods. All arguments
should be checked.
• Partial credit may be given for style, comments and readability.
BinaryNumber
private int data[]
private boolean overflow
public BinaryNumber(int length)
public BinaryNumber(String str)
public int getLength()
public int getDigit(int index)
public void shiftR(int amount)
public void add(BinaryNumber aBinaryNumber)
public String toString()
public int toDecimal()
public void clearOverflow()
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