Hello...  this is the way to write......

// Add two ints using bitwise operators

public class ArithWithBitOps {
  
//------------------------------------------------------------------------------
   // Second attempt  -  Go bit by bit right to left doing
binary arith
   static int carry = 0;  // c=1 for 1+1

   static int add2(int a, int b) {
      int sum = 0;                     // get sum here
      int mask = 1;                    // shifting mask used
to test each bit

      while(mask != 0) { 
         int ta = a & mask;                  // get next bit
to add
         int tb = b & mask;                  // get next bit
to add
         int bsum = bitAdd2(ta, tb, mask);   // add the bits
& set carry
         if(Testing) System.out.print("ta=" + ta + ", tb=" +
tb + ", bsum=" + bsum 
                           + ", carry=" + carry + ", b4sum="
+ sum);
         sum = (sum | bsum);                 // OR in the
results
         if(Testing) System.out.println(", aft sum=" + sum);
         mask = mask << 1;                   // move to next bit
      } // end while() thru bits

      if(carry > 0) System.err.println(">>>>>>>>>>>>losing
carry");
      return sum;
   } // end add2()

   //----------------------------------------------------------
   // Add two selected  bits in x and y & set carry if carry
   static int bitAdd2(int x, int y, int bsel) {
//      System.out.println("bitAdd2 of " + x + " " + y);
      int tx = x & bsel;
      int ty = y & bsel;
      if(carry == 1) {  // Have carry ?
         if((tx & ty) != 0) {
            carry = 1;
            return bsel;    // 1 + 1 + c=1 -> 1 + c=1
         }else if((tx ^ ty) != 0) {
            carry = 1;
            return 0;      // 1 + 0 + c=1 -> 0 + c=1
         }else {
            carry = 0;
            return bsel;   // 0 + 0 + c=1 -> 1 + c=0
         }
      }else if (carry == 0) { // no carry
         if((tx & ty) > 0) {
            carry = 1;
            return 0;      // 1 + 1 + c=0 -> 0 + c=1
         }else if((tx ^ ty) != 0) {
            carry = 0;
            return bsel;   // 1 + 0 + c=0 -> 1 + c=0
         }else {
            System.out.println("(tx ^ ty)=" + (tx ^ ty));
            carry = 0;
            return 0;      // 0 + 0 + c=0 -> 0 + c=0
         }
      }else {
         System.err.println("Invalid carry= " + carry);
         return 0;
      }
   } // end bitAdd2()

   //------------------------------------------------
   // Test the above
   public static void main(String[] args) {
      // The numbers to add
      int x = -24;
      int y = 15;

      if(Testing) System.out.println("Max int=" +
Integer.MAX_VALUE   //Max int=2147483647
           + " " + Integer.toHexString(-2)  //-2=fffffffe
           + " " + 0x80000000);    //-2147483648
      int sum = add2(x, y);
      System.out.println("Final sum= " + sum + " vs " + (x +
y) + "    " + Integer.toHexString(sum));
                        //Final sum= -9 vs -9    fffffff7  
   } // end main()

   static final boolean Testing = false;  // global flag for
debug output
}

public class BitWiseOpsExample {

public static int add(int x, int y) {

int xor, and, temp;
and = x & y; /* Obtain the carry bits */
xor = x ^ y; /* resulting bits */

while(and != 0 ) /* stop when carry bits are gone */
{
and <<= 1; /* shifting the carry bits one space */
temp = xor ^ and; /* hold the new xor result bits*/
and &= xor; /* clear the previous carry bits and assign the
new carry bits */
xor = temp; /* resulting bits */
}
return xor; /* final result */
}


public static void main(String[] args) {
System.out.println("Add 4 + 7");
System.out.println(add(4,7));

System.out.println("Add 25 + 25");
System.out.println(add(25,25));

}

}