We know that the size of the numbers that can be stored in the computer's memory cells is limited$.$ A memory cell of type long can store an integer up to a size of $263($about $16$ billion, a number with $11$ digits$).$

But we cannot store in a single memory cell the number $323445645332329488575477890349030.$

In this exercise, a class named BigNum will be built that will represent large non$-$negative numbers by an array. Each digit in the number will be stored in a cell in the array, with the leftmost digit $($MSB$)$ stored in cell number $0.$ Since the array will be of fixed size, each cell in the array that does not contain digits from the number will contain the The number $1.$ For example, the number $23125$ would be stored in the array like this:

$23125-1-1-1-1-1$

$0123456789$

question $1$ :

Write the BigNum class in JAVA to represent a large number as described. The class will contain a single attribute:

num $$ of type int$[].$

Define the MAX$\_$DIGITS constant in the class to indicate the maximum number of digits that can be stored in a number. Initialize it to $50.$

Added the following constructors to the class:

public BigNum$()$ an empty constructor that will initialize the number to $0.($Note that $0$ is represented by an array whose first cell has $0$ and all other cells have $1-).$

public BigNum$($long n$)$ the constructor will accept as a parameter a number of type long and insert its digits into the array.

Add the following methods to the class:

public String toString$()$ the method will return the number in the form of a string where a comma will appear after every three digits on the right. For example, if the number is $23125$ represented in the array above, the toString method will return the string $"23,125".$ Note that if the number contains three or fewer digits, no commas will appear in the string.

public int getNumOfDigits$()$ the method will return the number of digits of the number. For example, for the number $23125$ the method will return $5.$

public boolean equals$($BigNum n$)$ the method will accept as a parameter an object of type BigNum and return true if this is equal to n$,$ and false if not.

public BigNum add$($BigNum n$)$ the method will receive as a parameter an object of type BigNum and perform a connection between n and this. The method will return the result as a new object of type BigNum. Note, if the result of the concatenation creates a number with more digits than MAX$\_$DIGITS the method will return null.

public BigNum add$($int n$)$ the method will accept an integer n as a parameter and connect it to the number represented by this and return the result as a new BigNum object.

public BigNum plusplus$()$ the method will add $1$ to the number represented by this and return the result as a new object of type BigNum.

public BigNum multiply$($BigNum n$)$ the method will receive as a parameter an object of type BigNum and return the product of n in this. The method will return the result as a new object of type BigNum

public BigNum mod$($BigNum n$)$ the method will receive as a parameter an object of type BigNum and return the remainder from dividing this by n$,$ as a new object of type BigNum.

JAVA PLEASE