Binary to Decimal Conversion in C++

Binary to Decimal Conversion

Binary to Decimal conversion is the process of converting a binary number (base-2) into its equivalent decimal number (base-10). Each binary digit represents a power of 2.

For example, the binary number 1010 is equal to decimal 10 because:

(1 × 2³) + (0 × 2²) + (1 × 2¹) + (0 × 2⁰) = 8 + 0 + 2 + 0 = 10

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

Method 1: Using Loop

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

int binaryToDecimal(long long n) {
    int decimal = 0, i = 0;
    while (n != 0) {
        int lastDigit = n % 10;
        decimal += lastDigit * pow(2, i);
        n /= 10;
        i++;
    }
    return decimal;
}
            

Output:

Enter a binary number: 1010
Decimal equivalent (Loop): 10

Method 2: Using Recursion

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

int binaryToDecimalRecursive(long long n, int i) {
    if (n == 0)
        return 0;
    return (n % 10) * pow(2, i) + binaryToDecimalRecursive(n / 10, i + 1);
}
            

Output:

Enter a binary number: 1010
Decimal equivalent (Recursion): 10

Method 3: Using Bitwise Operations

#include <iostream>
using namespace std;

int binaryToDecimalBitwise(int n) {
    int decimal = 0, base = 1;
    while (n > 0) {
        int lastDigit = n % 10;
        decimal += lastDigit * base;
        base *= 2;
        n /= 10;
    }
    return decimal;
}
            

Output:

Enter a binary number: 1010
Decimal equivalent (Bitwise): 10

Main Function

#include <iostream>
using namespace std;

int main() {
    long long binary;
    cout << "Enter a binary number: ";
    cin >> binary;
    
    cout << "Decimal equivalent (Loop): " << binaryToDecimal(binary) << endl;
    cout << "Decimal equivalent (Recursion): " << binaryToDecimalRecursive(binary, 0) << endl;
    cout << "Decimal equivalent (Bitwise): " << binaryToDecimalBitwise(binary) << endl;
    
    return 0;
}