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.

`<script>`

`// Javascript 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`

` `

`let 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`

` `

`document.write(Add(15, 32));`

` `

`</script>`

**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);`

`}`