C++ Program For Octal To Decimal Conversion

Given an octal number, the task is to convert it into its equivalent decimal value. This can be done manually using powers of 8 or directly using C++'s stoi() function.

• The arithmetic approach processes each octal digit using powers of 8.
• The stoi() approach uses the built-in base-conversion functionality provided by C++.

Examples:

Input : 67
Output: 55

Input : 512
Output: 330

Approaches to Convert Octal to Decimal

The conversion can be performed using the following two approaches:

1. Using the Arithmetic Method

The idea is to process the octal number from right to left. Each digit is multiplied by the corresponding power of 8, starting with (8^0), and the results are added to obtain the decimal value.

Steps:

1. Initialize decValue to 0 and base to 1, representing (8^0).
2. Extract the last digit of the octal number.
3. Multiply the digit by the current base and add it to decValue.
4. Remove the last digit from the number.
5. Multiply base by 8 for the next position.
6. Repeat until all digits are processed.

#include <iostream>
using namespace std;

// Function to convert octal to decimal
int octalToDecimal(int n)
{
    int decimalValue = 0;
    int base = 1; // 8^0

    while (n > 0)
    {
        // Extract the last digit
        int lastDigit = n % 10;

        // Add digit × current power of 8
        decimalValue += lastDigit * base;

        // Move to the next power of 8
        base *= 8;

        // Remove the last digit
        n /= 10;
    }

    return decimalValue;
}

int main()
{
    int n = 67;

    cout << octalToDecimal(n);

    return 0;
} 

55

Explanation: For 67, the program first extracts 7 and multiplies it by (8^0). It then extracts 6 and multiplies it by (8^1). Adding these values gives the decimal equivalent 55.

Note: This approach treats the input as an integer. Therefore, it does not preserve leading zeros. For very large octal values, using a string is more appropriate.

2. Using the stoi() Function

C++ provides the stoi() function to convert a string into an integer using a specified number base. By passing 8 as the base, the function interprets the input string as an octal number and returns its decimal equivalent.

#include <iostream>
#include <string>
using namespace std;

// Function to convert octal string to decimal
int octalToDecimal(const string& n)
{
    return stoi(n, nullptr, 8);
}

int main()
{
    string n = "67";

    cout << octalToDecimal(n);

    return 0;
} 

55

Explanation: The string "67" is passed to stoi() with base 8. The function interprets 67 as an octal number and converts it directly to its decimal value, which is 55.

Note: stoi() returns an int. For values larger than the int range, use stol() or stoll() as appropriate.