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int Add(int x, int y)
{ 
    while (y != 0)
    {
        int carry = x & y; 
        x = x ^ y;
        y = carry << 1;
    }
    return x;
}

Here is the code to mulitply two numbers using the bitwise opertators
vid mulitply_two_numbers(int n,int m){
int i=0;
int res = 0;
for(i=0;i< 32; i++){
if(n & 1 << i)
res= res + (m<<i);
}
printf(" %d*%d = %d", n,m, res);
}

package test;

import java.util.Stack;

public class BitWiseMultiplication {
	static int bit(int num) {
		StringBuffer sb = new StringBuffer();
		Stack<Integer> stack = new Stack<Integer>();
		
		while(num>=1) {
			stack.push(num%2);
			num = num/2;
		}
		while(!stack.isEmpty()) {
			sb.append(stack.pop());
		}
		return Integer.valueOf(sb.toString());
	}
	
	static int bitAdd(int a, int b) {
		Stack<Integer> stack = new Stack<Integer>();
		int remainder = 0;
		while (a>=1 || b>=1) {
			int temp = (a%10)+(b%10)+remainder;
			if (temp <= 1) {
				stack.push(temp);
			} else {
				stack.push(0);
				remainder=1;
			}
			a=a/10;
			b=b/10;
		}
		StringBuffer sb = new StringBuffer();
		while(!stack.isEmpty()) {
			sb.append(stack.pop());
		}
		return Integer.valueOf(sb.toString());
	}
	
	static int convertBitToInt(int bitNum) {
		int i=0;
		int result = 0;
		while(bitNum>=1) {
			result += Math.pow(2, i)*(bitNum%10);
			bitNum = bitNum/10;
			i++;
		}
		return result;
	}
	public static void main(String[] args) {
		int a = 9;
		int b = 2;
		int bitA = bit(a);
		int bitB = bit(b);
		System.out.println("Num A:: "+a);
		System.out.println("Num B:: "+b);
		System.out.println("Bit A:: "+bitA);
		System.out.println("Bit B:: "+bitB);
		
		int bitMulResult = bitA*bitB;
		System.out.println("Bit Mul Result:: "+bitMulResult);
		
		int bitAddResult = bitAdd(bitA, bitB);
		System.out.println("Bit Add Result:: "+bitAddResult);
		
		int mulResult = convertBitToInt(bitMulResult);
		System.out.println("Int Mul Result:: "+mulResult);
		
		int addResult = convertBitToInt(bitAddResult);
		System.out.println("Int Result:: "+addResult);
	}
}

package test;

import java.util.Stack;

public class BitWiseOperations {
	static int bit(int num) {
		StringBuffer sb = new StringBuffer();
		Stack<Integer> stack = new Stack<Integer>();
		
		while(num>=1) {
			stack.push(num%2);
			num = num/2;
		}
		while(!stack.isEmpty()) {
			sb.append(stack.pop());
		}
		return Integer.valueOf(sb.toString());
	}
	
	static int bitAdd(int a, int b) {
		Stack<Integer> stack = new Stack<Integer>();
		int remainder = 0;
		while (a>=1 || b>=1) {
			int temp = (a%10)+(b%10)+remainder;
			remainder=0;
			if (temp <= 1) {
				stack.push(temp);
			} else {
				stack.push(0);
				remainder=1;
			}
			a=a/10;
			b=b/10;
		}
		if (remainder == 1) {
			stack.push(1);
		}
		StringBuffer sb = new StringBuffer();
		while(!stack.isEmpty()) {
			sb.append(stack.pop());
		}
		return Integer.valueOf(sb.toString());
	}
	
	static int convertBitToInt(int bitNum) {
		int i=0;
		int result = 0;
		while(bitNum>=1) {
			result += Math.pow(2, i)*(bitNum%10);
			bitNum = bitNum/10;
			i++;
		}
		return result;
	}
	public static void main(String[] args) {
		int a = 4;
		int b = 4;
		int bitA = bit(a);
		int bitB = bit(b);
		System.out.println("Num A:: "+a);
		System.out.println("Num B:: "+b);
		System.out.println("Bit A:: "+bitA);
		System.out.println("Bit B:: "+bitB);
		
		int bitMulResult = bitA*bitB;
		System.out.println("Bit Mul Result:: "+bitMulResult);
		
		int bitAddResult = bitAdd(bitA, bitB);
		System.out.println("Bit Add Result:: "+bitAddResult);
		
		int mulResult = convertBitToInt(bitMulResult);
		System.out.println("Int Mul Result:: "+mulResult);
		
		int addResult = convertBitToInt(bitAddResult);
		System.out.println("Int Result:: "+addResult);
	}
}

public static int multiply(int x, int y) {
    return ((x & 1) > 0 ? y : 0) + ((x & ~1) > 0 ? multiply(x >> 1, y << 1) : 0);
}

public static int multiply(int x, int y) {
    if (y == 0 || x == 0) {
        return 0;
    }
    if (x == 1) {
        return y;
    } else {
        return multiply(x >> 1, y << 1);
    }
}

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Bitwise Multiplication

public int Multiplication(int i, int j)
        {
            // take small number as 2nd number to make it faster
            if (i < j)
            {
                int temp = i;
                i = j;
                j = temp;
            }

            int totalBits = 0;
            int m = 0;

            // calculate bits in 2nd number
            while (Math.Pow(2, m) < j)
            {
                totalBits++;
                m++;
            }

            int sum = 0;
            int carry = 0;

            for (int n = 0; n < totalBits; n++)
            {
                // Making AND between 2nd number and numbers 1, 2, 4, 8 .. to detect whether bit    in a specific location in 2nd number is '0' or '1'
                int digit = j & (int)Math.Pow(2, n);

                //If bit in 2nd number is '1' then only do below operation
                if(digit > 0)
                {
                    // this is considering both numbers are 8 bits
                    digit = 255;

                    // Below operation is same when we do a decimal multiplication
                    carry = ((digit & i) << n) & sum;
                    sum = ((digit & i) << n) ^ sum;

                    while (carry != 0)
                    {
                        int newCarry = sum & (carry << 1);
                        sum = sum ^ (carry << 1);
                        carry = newCarry;
                    }
                }               
            }

            return sum;
        }