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.

Following is 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);`

`}`

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