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 most significant one: it represents the decimal number 123 +022 +121 +120 = 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.

1

An operation int getLength() for determining the length of a binary number.

An operation int[] getInnerArray() that returns the integer array representing the bi-

nary 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)

01101 + 01001

= 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.

2

1 1 1 (carried digits) 10110

+ 11101 =110011 =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 0s 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.

CODE MUST IMPLEMENT THE FOLLOWING UML CHART WHICH IS BELOW

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()