Binary Exponentiation

As the name suggests, it is the computation of a numerical or a binary component whose result can be as little as zero or as complex as ten raised to 18. The binary exponentiation concept utilizes two pillar extracts of exponentiation. We have learned in our lower grades that every numerical can be expressed in powers of sum or power notation of the numerical.

The two extracts help us get an edge over the traditional brute force notation representation of the binary digit's computation. In this article, we are deep diving into the concept of binary exponentiation in the C++ programming language.

Algorithm

// In this tutorial, we are going to learn about the concept of binary 
// exponentiation in C++ programming language with its relevant code and 
// output supported by comments and syntax, the below algorithm depicts
// the binary exponentiation in simpler terms 
POWER(a,b) :
    if b==0 :{
        return 1
    }
// function to calculate and return the answer to the main driver code
    else if b is odd :{
// if the initial condition fails, we compute for the next best edge case
        return a*POWER(a,(b-1)/2)*POWER(a,(b-1)/2)
    }
    else :{
// if the initial condition fails, we compute for the next best edge case
        return POWER(a,b/2)*POWER(a,b/2)
    }   

C++ code

// In this tutorial, we are going to learn about the concept of binary 
// exponentiation in C++ programming language with its relevant code and 
// output supported by comments and syntax 
#include <iostream>
using namespace std;
// function to calculate and return the answer to the main driver code
int exponent(int a, int b){
    
// this is our recursive base case when the variable b turns to 0
    if(b==0){
// universal fact a numerical which is raised to 0 is always one for sure
        return 1;
    }
    
// if the initial condition fails, we compute for the next best edge case
// b-1 operating b-1, which returns a and the answer to the main driver
// code functionality 
    
 // Here, we have created variables a and b which will store 'a' raised 
// to the power of 'b.'
    int answer = a * exponent(a,b-1);
    
    return answer;
}
// The main driver code functionality starts from here
int main() {
	
// Here, we have created variables a and b, which will compute a raised 
// to the power of b
	int a = 44, b = 8;
	
// Here, we are calling the  variables a and b, which will compute a raised 
// to the power of b
	cout<<"44 raised to the power 8 is : "<<exponent(a,b)<<endl;
// the main driver code functionality ends from here	
	return 0;
}

Output:

44 raised to the power eight is: -614400000

C++ code

// In this article, we are going to learn about the concept of binary 
// exponentiation in C++ programming language with its relevant code and 
// output supported by comments and syntax 
#include <iostream>
using namespace std;

// function to calculate and return the answer to the main driver code
// operating a raised to the power of b
int power (int a, int b){
// this is our recursive base case when the variable b turns to 0
    if(b==0){
        return 1;
    }
    //edge case cementing if the variable b turns out to be odd
    else if(b%2==1){
        return a*power(a,(b-1)/2)*power(a,(b-1)/2);
    }
//edge case cementing if the variable b turns out to be even
    else{
        return power(a,b/2)*power(a,b/2);
    }
}
// The main driver code functionality starts from here
int main() {
	
// Here, we have created variables a and b, which will compute a raised 
// to the power of b

	int a = 15 , b = 23;
	
	// here, we are trying to output the answer
	cout<<"15 raised to the power 23 is: "<<power(a,b)<<endl;
	
	return 0;
// The main driver code functionality starts from here
 }

Output:

15 raised to the power 23 is: 300332143

C++ code

#include <iostream>
using namespace std;

int main() {
	int a = 35 , b = 28;
	int answer = 1;
	while(b>0){
	    if(b%2==1){
	        answer = answer*a;
	        a = a*a;
	    }
	    else{
	        a = a*a;
	    }
	    b = b/2;
	    
	}
	cout<<"35 raised to the power 28 is: "<<answer<<endl;
	return 0;
}

Output:

35 raised to the power 28 is: -1049643599

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