# Add two numbers without using arithmetic operators using Javascript

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);`

`}`