## 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

3

• 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()