Description
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∗20 +0∗21 +1∗22 +1∗23 = 13. This is called little-endian format. You may use bigendian 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.
• 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.
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• 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.
1 Source: https://en.wikipedia.org/wiki/Binary_number
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• 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.
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()
