# Russian Peasant (Multiply two numbers using bitwise operators)

Given two integers, write a function to multiply them without using multiplication operator.

There are many other ways to multiply two numbers (For example, see this). One interesting method is the Russian peasant algorithm. The idea is to double the first number and halve the second number repeatedly till the second number doesn’t become 1. In the process, whenever the second number become odd, we add the first number to result (result is initialized as 0)
The following is simple algorithm.

Let the two given numbers be 'a' and 'b'
1) Initialize result 'res' as 0.
2) Do following while 'b' is greater than 0
a) If 'b' is odd, add 'a' to 'res'
b) Double 'a' and halve 'b'
3) Return 'res'.

## C/C++

 #include using namespace std;    // A method to multiply two numbers using Russian Peasant method unsigned int russianPeasant(unsigned int a, unsigned int b) {     int res = 0;  // initialize result        // While second number doesn't become 1     while (b > 0)     {          // If second number becomes odd, add the first number to result          if (b & 1)              res = res + a;             // Double the first number and halve the second number          a = a << 1;          b = b >> 1;      }      return res; }    // Driver program to test above function int main() {     cout << russianPeasant(18, 1) << endl;     cout << russianPeasant(20, 12) << endl;     return 0; }

## Java

 // Java program for Russian Peasant Multiplication import java.io.*;    class GFG  {     // Function to multiply two      // numbers using Russian Peasant method     static int russianPeasant(int a, int b)     {         // initialize result         int res = 0;               // While second number doesn't become 1         while (b > 0)         {              // If second number becomes odd,               // add the first number to result              if ((b & 1) != 0)                  res = res + a;                 // Double the first number              // and halve the second number             a = a << 1;             b = b >> 1;         }         return res;     }            // driver program     public static void main (String[] args)      {         System.out.println(russianPeasant(18, 1));         System.out.println(russianPeasant(20, 12));     } }    // Contributed by Pramod Kumar

## Python 3

 # A method to multiply two numbers # using Russian Peasant method    # Function to multiply two numbers  # using Russian Peasant method def russianPeasant(a, b):        res = 0 # initialize result        # While second number doesn't     # become 1     while (b > 0):                # If second number becomes         # odd, add the first number         # to result         if (b & 1):             res = res + a            # Double the first number          # and halve the second         # number         a = a << 1         b = b >> 1            return res    # Driver program to test # above function print(russianPeasant(18, 1)) print(russianPeasant(20, 12)) # This code is contributed by # Smitha Dinesh Semwal

## C#

 // C# program for Russian Peasant Multiplication using System;    class GFG {            // Function to multiply two     // numbers using Russian Peasant method     static int russianPeasant(int a, int b)     {         // initialize result         int res = 0;            // While second number doesn't become 1         while (b > 0) {                            // If second number becomes odd,             // add the first number to result             if ((b & 1) != 0)                 res = res + a;                // Double the first number             // and halve the second number             a = a << 1;             b = b >> 1;         }         return res;     }        // driver program     public static void Main()     {         Console.WriteLine(russianPeasant(18, 1));         Console.WriteLine(russianPeasant(20, 12));     } }    // This code is contributed by Sam007.

## PHP

 0)     {                    // If second number becomes odd,          // add the first number to result         if (\$b & 1)             \$res = \$res + \$a;            // Double the first number and          // halve the second number         \$a = \$a << 1;         \$b = \$b >> 1;     }     return \$res; }        // Driver Code     echo russianPeasant(18, 1), " ";     echo russianPeasant(20, 12), " ";        // This code is contributed by Ajit  ?>

/div>

Output:

18
240

How does this work?
The value of a*b is same as (a*2)*(b/2) if b is even, otherwise the value is same as ((a*2)*(b/2) + a). In the while loop, we keep multiplying ‘a’ with 2 and keep dividing ‘b’ by 2. If ‘b’ becomes odd in loop, we add ‘a’ to ‘res’. When value of ‘b’ becomes 1, the value of ‘res’ + ‘a’, gives us the result.
Note that when ‘b’ is a power of 2, the ‘res’ would remain 0 and ‘a’ would have the multiplication. See the reference for more information.

## tags:

Bit Magic Mathematical Mathematical Bit Magic