Hexadecimal to Octal Conversion

Hexadecimal to Octal Conversion” is a one of the classic programming problem exercise. Here, we are given a hexadecimal number, entered by user and our task is to write a program to convert the given hexadecimal number to its equivalent octal number.

Example:

HEXADECIMAL = 32A
OCTAL = 1452

The steps required to convert Hexadecimal number to Octal number are as follows:

  1. Scan the hexadecimal number from left to right digit by digit.
  2. Convert each digit of hexadecimal number into its corresponding 4-digit binary number, combine them and store it into temporary variable ‘hexadecimal_binary’.
  3. Make sure the number of digits of ‘hexadecimal_binary’ are divisible by 3. If not, add extra remaining 0s in the front of ‘hexadecimal_binary’.
  4. Now, distribute the ‘hexadecimal_binary’ into pairs of 3-digit binary numbers.
  5. Then, convert each 3-digit pair into corresponding Octal number.
  6. Combine the character and get the result.
  7. Print the result.

C++ Program to convert the hexadecimal to octal is as follows:

/* C++ Program to Convert Hexadecimal Number to Octal Number */  
#include<bits/stdc++.h>  
using namespace std;  
int bin2Dec(string binary)  
{  
    int decimal = 0;    
    int iterator = 2;     
    for(int i = 0; i < 3; i++)    
    {  
          
        char digit = binary[i];  
        if(digit == '1')  
        decimal = decimal + (1 * pow(2,iterator)); /* Putting it into formula */    
        iterator--;    
    }    
    return decimal;    
}  
int main()  
{  
    /* Scan the hexadecimal Number */  
    string Hexadecimal;  
    cout<<"Enter the Hexadecimal Number: ";  
    cin>>Hexadecimal;  
      
    /* Converting Hexadecimal to octal*/  
    string hexadecimal_binary;  
    /* Converting each digit of hexadecimal number 
       to 4-digit binary number and store the  
       combined result into 'hexadecimal_binary'  
    */  
    for(int i = 0; i < Hexadecimal.length(); i++)  
    {  
        string temp;  
        switch(Hexadecimal[i])  
        {  
            case '0': temp = "0000";  
            break;  
            case '1': temp = "0001";  
            break;  
            case '2': temp = "0010";  
            break;  
            case '3': temp = "0011";  
            break;  
            case '4': temp = "0100";  
            break;  
            case '5': temp = "0101";  
            break;  
            case '6': temp = "0110";  
            break;  
            case '7': temp = "0111";  
            break;  
            case '8': temp = "1000";  
            break;  
            case '9': temp = "1001";  
            break;  
            case 'A': temp = "1010";  
            break;  
            case 'B': temp = "1011";  
            break;  
            case 'C': temp = "1100";  
            break;  
            case 'D': temp = "1101";  
            break;  
            case 'E': temp = "1110";  
            break;  
            case 'F': temp = "1111";  
        }  
        /* Combining the 3-digit binary numbers */  
        hexadecimal_binary = hexadecimal_binary + temp;  
    }  
      
    /* Length of 'hexadecimal_binary' must be multiple of 3 */  
    if(hexadecimal_binary.length() % 3 != 0)  
    {  
        /* Inserting Extra 0s in front, if needed */  
        while(hexadecimal_binary.length() % 3 != 0)  
        {  
            hexadecimal_binary.insert(0,"0");  
        }  
    }  
  
    /* Distribute 'hexadecimal_binary' into pairs of 3-digit, 
       convert them into decimal equivalent which will be octal 
       equivalent 
    */  
    string Octal;  
    for(int i = 0; i < hexadecimal_binary.length(); i=i+3)  
    {  
        string temp = "";  
        temp+= hexadecimal_binary[i];  
        temp+= hexadecimal_binary[i+1];  
        temp+= hexadecimal_binary[i+2];  
          
        /* Converting 'temp' into decimal */  
        int decimal = bin2Dec(temp);  
          
        /* Converting decimal to corresponding Hexadecimal */  
        switch(decimal) {  
            case 0 :   
                Octal = Octal + '0';  
                break;  
            case 1 :   
                Octal = Octal + '1';  
                break;  
            case 2 :   
                Octal = Octal + '2';  
                break;  
            case 3 :   
                Octal = Octal + '3';  
                break;  
            case 4 :   
                Octal = Octal + '4';  
                break;  
            case 5 :   
                Octal = Octal + '5';  
                break;  
            case 6 :   
                Octal = Octal + '6';  
                break;  
            case 7 :   
                Octal = Octal + '7';  
                break;  
        }  
    }  
      
    /* Truncating Extra 0s from beginning, if any */  
    while(Octal[0]=='0')  
    {  
        Octal.erase(Octal.begin()+0);  
    }  
      
    /*Printing the result */  
    cout<<"The Octal of "<<Hexadecimal<<" is "<<Octal;  
}  

OUTPUT:
Enter the Hexadecimal number: 32A
The Octal of 32A is 1452

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