Decimal to Octal Conversion in C++

Decimal to Octal Conversion

Decimal to Octal conversion is the process of converting a decimal number (base-10) into its equivalent octal number (base-8). Each octal digit represents a power of 8.

For example, the decimal number 31 is equal to octal 37 because:

(3 × 8¹) + (7 × 8⁰) = 24 + 7 = 31

We will explore three methods to convert a decimal number to an octal number using C++ programming.

Method 1: Using Division by 8

We divide the decimal number by 8 repeatedly, storing the remainders. These remainders represent the digits of the octal number from least significant to most significant.

#include <iostream>
#include 
using namespace std;

void decimalToOctal(int decimal) {
    vector octal;
    
    while (decimal > 0) {
        octal.push_back(decimal % 8);
        decimal = decimal / 8;
    }
    
    cout << "Octal equivalent: ";
    for (int i = octal.size() - 1; i >= 0; i--) {
        cout << octal[i];
    }
    cout << endl;
}

int main() {
    int decimal;
    cout << "Enter a decimal number: ";
    cin >> decimal;
    decimalToOctal(decimal);
    return 0;
}
            

Output:

Enter a decimal number: 31
Octal equivalent: 37

Method 2: Using std::oct (C++'s built-in feature)

C++ provides a built-in way to print numbers in octal format using the std::oct manipulator.

#include <iostream>
using namespace std;

int main() {
    int decimal;
    cout << "Enter a decimal number: ";
    cin >> decimal;
    
    cout << "Octal equivalent: " << std::oct << decimal << endl;
    return 0;
}
            

Output:

Enter a decimal number: 31
Octal equivalent: 37

Method 3: Using Recursion

We can convert a decimal number to octal recursively. The recursive function divides the number by 8 and prints the remainders, which form the octal digits.

#include <iostream>
using namespace std;

void decimalToOctalRecursive(int decimal) {
    if (decimal == 0) {
        return;
    }
    
    decimalToOctalRecursive(decimal / 8);
    cout << decimal % 8;
}

int main() {
    int decimal;
    cout << "Enter a decimal number: ";
    cin >> decimal;
    
    if (decimal == 0) {
        cout << "Octal equivalent: 0" << endl;
    } else {
        cout << "Octal equivalent: ";
        decimalToOctalRecursive(decimal);
        cout << endl;
    }
    return 0;
}
            

Output:

Enter a decimal number: 31
Octal equivalent: 37