Add two numbers without using arithmetic operators using PHP

Software Development
#1

Write a function Add() that returns sum of two integers. The function should not use any of the arithmetic operators (+, ++, –, -, … etc).
Sum of two bits can be obtained by performing XOR (^) of the two bits. Carry bit can be obtained by performing AND (&) of two bits.
Above is simple Half Adder logic that can be used to add 2 single bits. We can extend this logic for integers. If x and y don’t have set bits at same position(s), then bitwise XOR (^) of x and y gives the sum of x and y. To incorporate common set bits also, bitwise AND (&) is used. Bitwise AND of x and y gives all carry bits. We calculate (x & y) << 1 and add it to x ^ y to get the required result.

<?php

// PHP Program to add two numbers

// without using arithmetic operator

function Add( $x , $y )

{

// Iterate till there is

// no carry

while ( $y != 0)

{

// carry now contains common

//set bits of x and y

$carry = $x & $y ;

// Sum of bits of x and y where at

//least one of the bits is not set

$x = $x ^ $y ;

// Carry is shifted by one

// so that adding it to x

// gives the required sum

$y = $carry << 1;

}

return $x ;

}

// Driver Code

echo Add(15, 32);

?>

Output :

47

Following is the recursive implementation for the same approach.

int Add( int x, int y)

{

if (y == 0)

return x;

else

return Add( x ^ y, (x & y) << 1);

}