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.
# Python3 Program to add two numbers
# without using arithmetic operator
def Add(x, y):
# Iterate till there is no carry
while (y ! = 0 ):
# carry now contains common
# set bits of x and y
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
print (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);
}