Implement addition: Do not use addition, subtraction, multiplication, division

From: http://sllovewsy149.blog.163.com/blog/static/108734178201245114626125/

Reference: http://blog.csdn.net/morewindows/article/details/8710737

Q: Write an algorithm to add two numbers, but do not use addition (+) or other arithmetic operations.

A: First, consider how we add two decimal numbers.

759 + 674, get 323 without considering carry.

If we only consider carrying, we get 1110.

So we get 759 + 674 = 323 + 1110 = 1433

What does the computer do with the binary number?

Use an exclusive or (^) without considering carry)

If we only consider the carry, we use (&) and shift left (<) at the same time.

Use recursion until the carry value is 0. Then the sum of the two numbers is obtained.

The following is the Java code:

   1: public int addNoArithm(int a, int b) {

   2:     if (b == 0) {

   3:         return a;

   4:     }

   5:     int sum = a ^ b;

   6:     int carry = (a & b) << 1;

   7:     return addNoArithm(sum, carry);

   8: }

PS: we do not need to use arithmetic operations to obtain the sum of two numbers. We should first think of bitwise operations, because it seems that we have no other choice.