Hexadecimal to Decimal Conversion in C++

Hexadecimal to Decimal Conversion

Hexadecimal to Decimal conversion is the process of converting a hexadecimal number (base-16) into its equivalent decimal number (base-10). Each hexadecimal digit represents a power of 16.

For example, the hexadecimal number 1F is equal to decimal 31 because:

(1 × 16¹) + (F × 16⁰) = 16 + 15 = 31

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

Method 1: Using Loop

We extract each digit of the hexadecimal number, multiply it by the corresponding power of 16, and sum the results.

#include 
#include 
#include 
using namespace std;

int hexToDecimal(string hex) {
    int decimal = 0, base = 1;
    for (int i = hex.length() - 1; i >= 0; i--) {
        char digit = hex[i];
        int value = (digit >= '0' && digit <= '9') ? digit - '0' : digit - 'A' + 10;
        decimal += value * base;
        base *= 16;
    }
    return decimal;
}

int main() {
    string hex;
    cout << "Enter a hexadecimal number: ";
    cin >> hex;
    cout << "Decimal equivalent: " << hexToDecimal(hex) << endl;
    return 0;
}
            

Output:

Enter a hexadecimal number: 1F
Decimal equivalent: 31

Method 2: Using Built-in Function

We can use C++'s stoi() function with a base of 16 to directly convert a hexadecimal number to a decimal number.

#include 
#include 
using namespace std;

int main() {
    string hex;
    cout << "Enter a hexadecimal number: ";
    cin >> hex;
    
    int decimal = stoi(hex, nullptr, 16);
    cout << "Decimal equivalent: " << decimal << endl;
    return 0;
}
            

Output:

Enter a hexadecimal number: 1F
Decimal equivalent: 31

Method 3: Using Recursion

We recursively extract each digit and multiply it by the corresponding power of 16.

#include 
#include 
#include 
using namespace std;

int hexToDecimalRecursive(string hex, int length, int index) {
    if (index == length)
        return 0;
    char digit = hex[index];
    int value = (digit >= '0' && digit <= '9') ? digit - '0' : digit - 'A' + 10;
    return value * pow(16, length - index - 1) + hexToDecimalRecursive(hex, length, index + 1);
}

int main() {
    string hex;
    cout << "Enter a hexadecimal number: ";
    cin >> hex;
    
    cout << "Decimal equivalent: " << hexToDecimalRecursive(hex, hex.length(), 0) << endl;
    return 0;
}
            

Output:

Enter a hexadecimal number: 1F
Decimal equivalent: 31