CS 284: Homework Assignment 1Due: September 7, 11:55pm1 Assignment PoliciesCollaboration Policy. Homework will be done individually: each student must hand intheir own answers. It is acceptable for students to collaborate in understanding the materialbut not in solving the problems or programming. Use of the Internet is allowed, but shouldnot 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 and section .2 AssignmentDefine a class BinaryNumber that represents binary numbers and a few simple operations onthem, as indicated below. An example of a binary number is1011Its length is 4. Note that its leftmost digit is the most significant one: it represents thedecimal number 1 ∗ 23 + 0 ∗ 22 + 1 ∗ 21 + 1 ∗ 20 = 11. This is called big-endian format. Pleasebe sure to use big-endian format in your program.This assignment requests that a number of operations be supported. They are dividedinto two groups. The first is a set of basic operations, the second is slightly more challengingand addresses addition of binary numbers.2.1 Basic operationsThe following operations should be supported:• A constructor BinaryNumber(int length) for creating a binary number of length lengthand consisting only of zeros.• A constructor BinaryNumber(String str) for creating a binary number given a string. Forexample, 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 listedin 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 binarynumber.• An operation int getDigit(int index) for obtaining a digit of a binary number given anindex. The starting index is 0. If the index is out of bounds, then a message shouldbe 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 binarynumber any number of places to the left or right. The direction parameter indicatesa left shift when the value is -1. When direction is given the value 1, the shift shouldbe to the right. Any other value for direction should be seen as invalid. The amountparameter specifies how many digits the BinaryNumber will be shifted, and is onlyvalid 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 byfactors of 2, while shifting left increases the number by factors of 2. These operationsare equivalent to the ”>>” and ”<<” operators in Java.• An operation static int[] bwor(BinaryNumber bn1, BinaryNumber bn2) that computes thebitwise or of the two numbers. Note that both argument BinaryNumbers must be ofthe 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 thebitwise and of the two numbers. Note that both argument BinaryNumbers must be ofthe 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 correspondingencoded string.2.2 Addition of Binary NumbersHere 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 = 22Note that it is possible for the addition of two numbers to yield a result which has alarger 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_number21 1 1 (carried digits)1 0 1 1 0+ 1 1 1 0 1= 1 1 0 0 1 1 = 51The 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 binarynumber that receives the message and the other is given as a parameter. If the lengthsof the two BinaryNumbers do not coincide, then the smaller one should have 0’sprepended 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 withthe result of addition.2.3 Hints• For the BinaryNumber(String str) constructor, the following operations might come inhandy:– char java.lang.String.charAt(int index), which returns the char value at the specifiedindex. An index ranges from 0 to length() - 1. The first char value of thesequence 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 thatthe specified Unicode character represents.• For methods where allocating more space is necessary, it may be useful to define astatic void prepend(int amount) method, that preprends amount 0’s to the BinaryNumber.3 Submission instructionsSubmit 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 argumentsshould be checked.• Partial credit may be given for style, comments and readability.3BinaryNumberprivate int data[]private int lengthpublic 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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