What is the best way to add two numbers without using the + operator?

Question

A friend and I are going back and forth with brain-teasers and I have no idea how to solve this one. My assumption is that it\'s possible with some bitwise operators, but n

Answer 1

In python using bitwise operators:

def sum_no_arithmetic_operators(x,y):
    while True:
        carry = x & y
        x = x ^ y
        y = carry << 1
        if y == 0:
            break
    return x

Answer 2

Here's a portable one-line ternary and recursive solution.

int add(int x, int y) {
    return y == 0 ? x : add(x ^ y, (x & y) << 1);
}

Answer 3

Cheat. You could negate the number and subtract it from the first :)

Failing that, look up how a binary adder works. :)

EDIT: Ah, saw your comment after I posted.

Details of binary addition are here.

Answer 4

Here is the solution in C++, you can find it on my github here: https://github.com/CrispenGari/Add-Without-Integers-without-operators/blob/master/main.cpp

int add(int a, int b){
   while(b!=0){
      int sum = a^b; // add without carrying
      int carry = (a&b)<<1; // carrying without adding
      a= sum;
      b= carry;
    }
   return a;
 }
 // the function can be writen as follows :
 int add(int a, int b){
     if(b==0){
        return a; // any number plus 0 = that number simple!
    }
    int sum = a ^ b;// adding without carrying;
    int carry = (a & b)<<1; // carry, without adding
    return add(sum, carry);
  }

Answer 5

You can do it using bit-shifting and the AND operation.

#include <stdio.h>

int main()
{
    unsigned int x = 3, y = 1, sum, carry;
    sum = x ^ y; // Ex - OR x and y
    carry = x & y; // AND x and y
    while (carry != 0) {
        carry = carry << 1; // left shift the carry
        x = sum; // initialize x as sum
        y = carry; // initialize y as carry
        sum = x ^ y; // sum is calculated
        carry = x & y; /* carry is calculated, the loop condition is
                        evaluated and the process is repeated until
                        carry is equal to 0.
                        */
    }
    printf("%d\n", sum); // the program will print 4
    return 0;
}

Answer 6

Define "best". Here's a python version:

len(range(x)+range(y))

The + performs list concatenation, not addition.