How to add two numbers without using ++ or + or another arithmetic operator

Question

How do I add two numbers without using ++ or + or any other arithmetic operator?

It was a question asked a long time ago in some campus interview. Anyway, today someone asked a question regarding some bit-manipulations, and in answers a beautiful quide Stanford bit twiddling was referred. I spend some time studying it and thought that there actually might be an answer to the question. I don't know, I could not find one. Does an answer exist?

Answer 1

This is something I have written a while ago for fun. It uses a two's complement representation and implements addition using repeated shifts with a carry bit, implementing other operators mostly in terms of addition.

#include <stdlib.h> /* atoi() */ #include <stdio.h>  /* (f)printf */ #include <assert.h> /* assert() */  int add(int x, int y) {     int carry = 0;     int result = 0;     int i;      for(i = 0; i < 32; ++i) {         int a = (x >> i) & 1;         int b = (y >> i) & 1;         result |= ((a ^ b) ^ carry) << i;         carry = (a & b) | (b & carry) | (carry & a);     }      return result; }  int negate(int x) {     return add(~x, 1); }  int subtract(int x, int y) {     return add(x, negate(y)); }  int is_even(int n) {     return !(n & 1); }  int divide_by_two(int n) {     return n >> 1; }  int multiply_by_two(int n) {     return n << 1; }  int multiply(int x, int y) {     int result = 0;      if(x < 0 && y < 0) {         return multiply(negate(x), negate(y));     }      if(x >= 0 && y < 0) {         return multiply(y, x);     }      while(y > 0) {         if(is_even(y)) {             x = multiply_by_two(x);             y = divide_by_two(y);         } else {             result = add(result, x);             y = add(y, -1);         }     }      return result; }  int main(int argc, char **argv) {     int from = -100, to = 100;     int i, j;      for(i = from; i <= to; ++i) {         assert(0 - i == negate(i));         assert(((i % 2) == 0) == is_even(i));         assert(i * 2 == multiply_by_two(i));         if(is_even(i)) {             assert(i / 2 == divide_by_two(i));         }     }      for(i = from; i <= to; ++i) {         for(j = from; j <= to; ++j) {             assert(i + j == add(i, j));             assert(i - j == subtract(i, j));             assert(i * j == multiply(i, j));         }     }      return 0; }