addition without operators Algorithm
In mathematics and computer programming, the order of operations (or operator precedence) is a collection of rules that reflect conventions about which procedures to perform first in order to evaluate a given mathematical expression. For example, in mathematics and most computer languages, multiplication is granted a higher precedence than addition, and it has been this manner since the introduction of modern algebraic notation.
/**
* Addtion of two numbers without using any arithmatic operators.
*/
#include <iostream>
int sum( int x, int y ) {
int carry = 0;
while( y != 0 ) {
//if x and y don't have same bits at same position, XOR of x and y
//gives us sum of x and y at those positions.
// bits wont change at positions containing same bits, however,
// we have to incorporate carry bits. AND of x and y gives all carry bits.
// carry will be added from position 1 (not 0), so we need to shift carry
// by 1.
carry = x & y;
x = x ^ y;
y = carry << 1;
}
return x;
}
//recursive version
int sum2( int x, int y ) {
if ( y == 0 ) {
return x;
}
return sum2( x ^ y, (x & y) << 1);
}
int main()
{
int x , y;
std::cout << "Addition of two numbers without using arithmatic operators:\n";
std::cout << "Enter num 1 :" ;
std::cin >> x;
std::cout << "Enter num 2 :" ;
std::cin >> y;
std::cout << "Iterative version - Addition of " << x << " and " << y
<< " is " << sum(x, y) << std::endl;
std::cout << "Recursive version - Addition of " << x << " and " << y
<< " is " << sum2(x, y) << std::endl;
return 0;
}
