Description
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 most significant one: it represents the
decimal number 1 ∗ 2
3 + 0 ∗ 2
2 + 1 ∗ 2
1 + 1 ∗ 2
0 = 11. This is called big-endian format. Please
be sure to use big-endian format in your program.
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[] getInnerArray() that returns the integer array representing the 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 bitShift(int direction, int amount) for shifting all digits in a binary
number any number of places to the left or right. The direction parameter indicates
a left shift when the value is -1. When direction is given the value 1, the shift should
be to the right. Any other value for direction should be seen as invalid. The amount
parameter specifies how many digits the BinaryNumber will be shifted, and is only
valid when it is nonnegative. For example, ’1011’ shifted right by 2 is ’10’. ’1011’
shifted left by 2 is ’101100’. Notice that shifting right decreases the number by
factors of 2, while shifting left increases the number by factors of 2. These operations
are equivalent to the ”>>” and ”<<” operators in Java.
• An operation static int[] bwor(BinaryNumber bn1, BinaryNumber bn2) that computes the
bitwise or of the two numbers. Note that both argument BinaryNumbers must be of
the same length for the input to be considered valid. The bitwise or of ’1010’ and
’1100’ is ’1110’.
• An operation static int[] bwand(BinaryNumber bn1, BinaryNumber bn2) that computes the
bitwise and of the two numbers. Note that both argument BinaryNumbers must be of
the same length for the input to be considered valid. The bitwise and of ’1010’ and
’1100’ is ’1000’.
• An operation String toString() that returns the BinaryNumber as the corresponding
encoded string.
2.2 Addition of Binary Numbers
Here is an example of how two binary numbers of the same length are added1
.
1 1 (carried digits)
0 1 1 0 1
+ 0 1 0 0 1
= 1 0 1 1 0 = 22
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, room should be made for the extra digit -
meaning the array should be copied over to a new one that is one greater in length.
1Source: https://en.wikipedia.org/wiki/Binary_number
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1 1 1 (carried digits)
1 0 1 1 0
+ 1 1 1 0 1
= 1 1 0 0 1 1 = 51
The int[] field data should be added to the data fields of 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 two BinaryNumbers do not coincide, then the smaller one should have 0’s
prepended to it in order to prevent errors. Note how ’101’ + ’1’ is the same as ’101’
+ ’001’. The BinaryNumber which receives aBinaryNumber should be modified with
the result of addition.
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 methods where allocating more space is necessary, it may be useful to define a
static void prepend(int amount) method, that preprends amount 0’s to the BinaryNumber.
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 (see below).
• 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.
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BinaryNumber
private int data[]
private int length
public BinaryNumber(int length)
public BinaryNumber(String str)
public int getLength()
public int getDigit(int index)
public int[] getInnerArray()
public static int[] bwor(BinaryNumber bn1, BinaryNumber bn2)
public static int[] bwand(BinaryNumber bn1, BinaryNumber bn2)
public void bitShift(int direction, int amount)
public void add(BinaryNumber aBinaryNumber)
public String toString()
public int toDecimal()
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