Add Numbers

Problem Statement:
         Add two given numbers without '+' operator.

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Solution:
      We will be adding two given numbers using 'AND' and 'XOR' logical operators.

Fig: Half Adder , S: Sum and C: Carry

Sum of two number can be achieved with Half adder, if carry is greater than 0 , then it the process is repeated again. This is half adder implementation.

and as per full adder implementation :
   Sum = 2*C + S

Below are the different ways of getting the sum using XOR and AND logical operators.

Method 1 : 

int add(int a, int b) {
  while (b != 0) {
   int carry = a & b;
   a = a ^ b;
   b = carry << 1;
  }
  return a;
 }

Method 2:

 int add(int a, int b) {
  if (b == 0)
   return a;
  else
   return add2(a ^ b, (a & b) << 1);
 }

Method 3:

  int add(int a,int b){
  int carry= a & b;
  int sum= a ^ b;
  
  carry = 2* carry;
  
  sum = sum ^ carry;
  
  return sum;
 }

Method 4:

 int add(int a,int b){
  return ( 2*( a & b) ) ^ (a ^ b);
 }

Please post your comment and suggestions.
Happy Coding !! :)


References: 
Wikipedia