Multiply Two Numbers Without Using Arithmetic Operator in Java

In this section, we will learn how to multiply two numbers without using the arithmetic operator (*) in Java.

The multiplication of two numbers can be found by the repeated addition method. It means that add the number (multiplicand) into itself up to multiplicator times. The method can be used if we want to calculate the multiplication of small numbers.

Suppose, we want to multiply 3 by 4 which gives 12 as the result. The same can be achieved by adding 3 four times i.e. (3 + 3 + 3 + 3 = 12) or by adding 4 three times i.e. (4 + 4 + 4 = 12). Both give the same result. Therefore, we can implement the logic using recursion.

Using for Loop

MultiplicationExample1.java

  import java.util.Scanner;  public class MultiplicationExample1  {  public static void main(String args[])   {  Scanner sc=new Scanner(System.in);  int x, y, sum=0;  System.out.print(“Enter the first number: “);  x=sc.nextInt();  System.out.print(“Enter the second number: “);  y=sc.nextInt();  //executes until the condition becomes false  for(int i=1;i<=x;i++)  {  //calculates the sum  sum=sum+y;  }  //prints the result  System.out.println(“The multiplication of “+x+” and “+y+” is: “+sum);  }  }  

Output:

Enter the first number: 6  Enter the second number: 16  The multiplication of 6 and 16 is: 96

Let’s see another logic for the same.

MultiplicationExample2.java

  import java.util.Scanner;  public class MultiplicationExample2  {  public static void main(String args[])  {  int product=0;  Scanner scan=new Scanner(System.in);   System.out.print(“Enter the first number: “);  int multiplicand = scan.nextInt();  System.out.print(“Enter the second number: “);  int multiplicator = scan.nextInt();  for(int i=0; i<multiplicator; i++)  {  product=sum(product, multiplicand);  }  System.out.print(“product of “+ multiplicand+” and “+ multiplicator +” is: “+product);  }  static int sum(int multiplicand, int multiplicator)  {  for(int i=0; i<multiplicator; i++)  multiplicand++;  return multiplicand;  }  }  

Output:

Enter the first number: 37  Enter the second number: 23  product of 37 and 23 is: 851

Using while Loop

MultiplicationExample3.java

  import java.util.Scanner;  public class MultiplicationExample3  {  public static void main(String args[])  {  int product=0;      Scanner scan = new Scanner(System.in);   System.out.print(“Enter the multiplicand: “);  //reads an integer from the user  int multiplicand = scan.nextInt();  System.out.print(“Enter the multiplicator: “);  //reads an integer from the user  int multiplicator=scan.nextInt();  for(int i=0; i<multiplicator; i++)  {  //calling user-defined function sum()      product = sum(product, multiplicand);  }  //prints the result  System.out.print(“The product of “+multiplicand+” and “+multiplicator+” is:  “+product);  }  //function that calculates the multiplication of two numbers  static int sum(int multiplicand, int multiplicator)  {  //executes if multiplicator is greater than 0      while(multiplicator != 0)  {  //applying bitwise AND operator      //if multiplicand is 60 (in binary 0011 1100) and multiplicator is 13 (in binary 0000 1101) then (multiplicand & multiplicator) will be 12 = 0000 1100      int x = (multiplicand & multiplicator);    //applying bitwise exclusive OR operator  multiplicand = multiplicand ^ multiplicator;  //applying left shift operator  multiplicator = x<<1;    //for example: (10<<2)=10*2^2=10*4=40    }  //returns multiplicand if multiplicator is 0  return multiplicand;  }  }  

Output:

Enter the multiplicand: 17  Enter the multiplicator: 8  The product of 17 and 8 is:  136

Using Recursion

By using the recursion, we can multiply two integers with the given constraints. To multiply a and b, recursively add a, b time.

Integers include both positive and negative numbers. The multiplier or multiplicand may hold a positive or a negative sign before the number. No sign before a number represents a positive number. If the number holds a positive or a negative sign, they follow the rules, given in the following table.

Multiply Two Numbers Without Using Arithmetic Operator in Java

The above table represents that:

The multiplication of two negative numbers gives a positive integer.
The multiplication of two positive numbers also gives a positive integer.
The multiplication of a positive and a negative number gives a negative integer.
The multiplication of a negative and a positive number gives a negative integer.

The following program also works if the numbers are negative.

MultiplicationExample4.java

  public class MultiplicationExample4  {  //function multiply two numbers a and b  static int product(int a, int b)   {  //checks b is 0 or not  if (b == 0)  //returns 0 if any number multiplied by 0  return 0;  //checks if b is greater than 0 or not  if (b > 0)  //calculates sum and return the same  return (a + product(a, b – 1));  //executes if b is negative  if (b < 0)  return -product(a, -b);  return -1;  }  //driver code  public static void main(String args[])   {  //calling user-defined function and print the result      System.out.println(“The multiplication is: ” + product(-5, 9));  System.out.println(“The multiplication is: ” + product(-8, -17));  System.out.println(“The multiplication is: ” + product(12, 12));  }  }  

Output:

The multiplication is: -45  The multiplication is: 136  The multiplication is: 144

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Multiply Two Numbers Without Using Arithmetic Operator in Java

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Using while Loop

Using Recursion

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