Sum of integers using XOR, AND gates

Question

How to compute sum of two integers using bit wise NOT, XOR, AND,and OR operators, without using SHIFT operator (not using arithmetic operators as well)? Is it possible ?

Example C code:

int a = 5;
int b = 11;
int c = a ^ b;
int d = a & b;
int sum = ...

Answer 1

Let's take a = b = 1 . The result of this sum is sum = 2 . The binary representation of the inputs are 00000001 (let's have 8-bits for simplicity). The output is 00000010 . You can easily get the least significant bit, LSB = a0 XOR b0 , but to modify the bit number 1 you need a shift.