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);`

`}`