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);
}