# Add two numbers without using arithmetic operators using Java

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.

`// Java Program to add two numbers`

`// without using arithmetic operator`

`import` `java.io.*;`

`class` `GFG`

`{`

` ` `static` `int` `Add(` `int` `x, ` `int` `y)`

` ` `{`

` ` `// Iterate till there is no carry`

` ` `while` `(y != ` `0` `)`

` ` `{`

` ` `// carry now contains common`

` ` `// set bits of x and y`

` ` `int` `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`

` ` `public` `static` `void` `main(String arg[])`

` ` `{`

` ` `System.out.println(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);`

`}`