# Add two numbers without using arithmetic operators using PHP

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);`

`}`