binary exponentiation

To perform binary exponentiation in C++, you can use the following algorithm:

Step 1: Initialize a variable 'result' to 1. Step 2: Iterate through the bits of the exponent in binary representation from right to left. Step 3: For each bit, perform the following operations: - Multiply 'result' by itself (result = result). - If the current bit is 1, multiply 'result' by the base value (result = base). Step 4: After iterating through all the bits, the final value of 'result' will be the result of exponentiation.

Here is an example to illustrate this algorithm:

#include <iostream>

using namespace std;

// Function to perform binary exponentiation
int binaryExponentiation(int base, int exponent) {
    int result = 1;

    while (exponent > 0) {
        if (exponent & 1) {
            result *= base;
        }

        base *= base;
        exponent >>= 1;
    }

    return result;
}

int main() {
    int base = 2;
    int exponent = 5;

    int result = binaryExponentiation(base, exponent);

    cout << base << " raised to the power of " << exponent << " is: " << result << endl;

    return 0;
}

In this example, we have a base value of 2 and an exponent value of 5. The binary representation of 5 is 101. Following the algorithm:

• In the first iteration, the result is multiplied by itself (result = 1 * 1 = 1).
• In the second iteration, the result is multiplied by the base value (result = 1 * 2 = 2).
• In the third iteration, the result is multiplied by itself again (result = 2 * 2 = 4).
• After iterating through all the bits, the final value of 'result' is 4, which is the result of 2 raised to the power of 5.