In this lesson, we have a challenge for you.

Binary conversion

Take an integer N, followed by a stream of N numbers. The stream should be loaded in an array. Then your program should calculate the binary representation of each number in a separate 2D array (where every binary representation should be stored in a single dimensional array along with its representation size on the first index of the array). In the end, the program should display each number’s binary representation.

Here’s the sample file:

Numbers.txt
-----------
5
8 15 3 28 47

Output:
Decimal   size  Binary    
8         4     1 0 0 0 
15        4     1 1 1 1 
3         2     1 1 
28        5     1 1 1 0 0 
47        6     1 0 1 1 1 1

Here’s the pictorial representation of the 2-D structures we would like to build:

  • An array, Numbers[], loaded with all decimal numbers from the file.
  • A 2-D map, where each row ri represents the size (the binary representation size of Numbers[ri]) followed by its binary representation.

Here’s the sample output of the program:

Decimal   size  Binary    
8         4     1 0 0 0 
15        4     1 1 1 1 
3         2     1 1 
28        5     1 1 1 0 0 
47        6     1 0 1 1 1 1

Playground for your implementation

Write your code below:

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main.cpp
Numbers.txt
#include <iostream>
#include <fstream>
#include <iomanip>
using namespace std;
#define MaxRows 100
#define MaxCols 100
#define Capacity 100
int binarySize(int aNumber)
{
	// Write your code here
}
void convertToBinary(int binaryMap[][MaxCols], int Numbers[], int size)
{
	// Write your code here
}
void displayBinary(int binaryMap[][MaxCols], int Numbers[], int size)
{
	// Write your code here
}
int main()
{
	ifstream Rdr("Numbers.txt");
	int size;
	Rdr >> size;
	int binaryMap[MaxRows][MaxCols];
	int Numbers[Capacity];
	for (int i = 0; i < size; i++)
	{
		Rdr >> Numbers[i];
	}
	convertToBinary(binaryMap, Numbers, size);
    displayBinary(binaryMap, Numbers, size);
	return 0;
}

Steps to follow for decimal to binary conversion

Let’s write our program step by step. We have turned it into tasks.

Task 1: Finding decimal to binary representation size

We should make a function:

int binarySize(int aNumber);

This function receives a decimal number and returns the size of its binary representation. For example, 2323 has a binary representation with 5 digits.

We will be needing this function while calculating the binary representation of each number.

Hint: Look at the animation below carefully. All you need to do is maintain a counter and keep dividing the given number by 2 until the number becomes zero. The number of times the repeated division happens is the exact size of the binary representation.

Instruction: Add the code for this task 1 in your playground.

Task 2: Converting each decimal number to binary and storing in the map

Now let’s make the following function:

void convertToBinary( int Numbers[], int size, int binaryMap[][MaxCols])

It has the following parameters:

  1. int Numbers[], int size: The list of decimal numbers, which we want to convert into binary representations.

  2. int binaryMap[][MaxCols]: For each decimal number in Numbers[], this function stores the binary representation in this map (where the zeroth index in each row represents the size of each binary representation followed by the actual representation).

Hint: Look at the animation below carefully. You need to do the following:

  • For each number Number[i],
    • Store the size of the binary representation at binaryMap[i][0], then keep dividing the number by 2 and along with that store the remainder in the reverse order in reverse order.

Look at the following animation for clarity:

Task 3: Displaying the number and its corresponding binary representation

You have to write the following function now:

void displayBin(int binaryMap[][MaxCols], int Numbers[], int size);

This function should display the following output:

Decimal   	Binary
 8  :   	1 0 0 0 
 15 :   	1 1 1 1 
 3  :    	1 1 
 28 :   	1 1 1 0 0 
 47 :   	1 0 1 1 1 1

Here's the complete animation of how the conversion will happen.

Complete implementation

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main.cpp
Numbers.txt
#include <iostream>
#include <fstream>
#include <iomanip>
using namespace std;
#define MaxRows 100
#define MaxCols 100
#define Capacity 100
int binarySize(int aNumber)
{
	int counter = 0;
	if (aNumber == 0)
		counter++;
	while(aNumber > 0)
	{
		aNumber = aNumber / 2;
		counter++;
	}
	return counter;
}
void convertToBinary(int binaryMap[][MaxCols], int Numbers[], int size)
{
	for (int i = 0; i < size; i++)
	{
	    int value = Numbers[i];
	    int counter = binarySize(Numbers[i]);
	    binaryMap[i][0] = counter;
	    for (int j = counter; j > 0; j--)
	    {
	        binaryMap[i][j] = value % 2;
	        value /= 2;
	    }
	}
}
void displayBinary(int binaryMap[][MaxCols], int Numbers[], int size)
{
    int binSize = 0;
    cout <<left<< setw(10)<< "Decimal" << setw(6) << "size" << setw(10) << "Binary"<<endl;
	for (int i = 0; i < size; i++)
	{
        binSize = binaryMap[i][0];
		cout << left << setw(10)<<Numbers[i] << setw(6) << binSize ;
		
		for (int j = 1; j <= binSize; j++)
			cout<<binaryMap[i][j] << " ";
		cout << endl;
	}
}
int main()
{
	ifstream Rdr("Numbers.txt");
	int size;
	Rdr >> size;
	int binaryMap[MaxRows][MaxCols];
	int Numbers[Capacity];
	for (int i = 0; i < size; i++)
	{
		Rdr >> Numbers[i];
	}
	convertToBinary(binaryMap, Numbers, size);
    displayBinary(binaryMap, Numbers, size);
	return 0;
}