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Code Mathematics

Number divisible by 8 using bitwise

To check whether a number is divisible by 8 using bitwise operators, we can use the fact that any number that is a multiple of 8 will have its last three bits set to 0.

Here's how you can check if a number is divisible by 8 using bitwise operators in Python:

def is_divisible_by_8(num):
    return (num & 0b111) == 0

To check if a number is divisible by 8 using bitwise shift, we can use the following condition:

A number is divisible by 8 if and only if its three least significant bits are all 0.

We can check the three least significant bits of a number by performing a bitwise AND operation with the binary number 7 (which is 111 in binary with three bits).

To do this using bitwise shift, we can right shift the number by 3 bits, which is equivalent to dividing the number by 8. Then, we can left shift the result by 3 bits to get back the original number, and perform a bitwise AND operation with 7 to check if the three least significant bits are all 0.

Here's an example implementation in Python:

def is_divisible_by_8(n):
    return (n >> 3) << 3 == n and (n & 7) == 0

This function takes a number n as input, right shifts it by 3 bits to divide it by 8, left shifts the result by 3 bits to get back the original number, and performs a bitwise AND operation with 7 to check if the three least significant bits are all 0.

Note that this implementation assumes that n is a non-negative integer. If n can be a negative number, we need to use arithmetic shift instead of logical shift to preserve the sign of the number.

Here another example.

/*
    C program for
    Number divisible by 8 using bitwise
*/
#include <stdio.h>

void divisibleBy8(int num)
{
    // Shift right by 3
    int auxiliary = num >> 3;
    // Shift left by 3
    auxiliary = auxiliary << 3;
    // Check if auxiliary is equal to number or not
    if (auxiliary == num)
    {
        printf("\n Number %d divisible by 8", num);
    }
    else
    {
        printf("\n Number %d is not divisible by 8", num);
    }
}
int main(int argc, char const *argv[])
{
    // Test Inputs
    divisibleBy8(56);
    divisibleBy8(31);
    divisibleBy8(32);
    divisibleBy8(72);
    divisibleBy8(78);
    return 0;
}

Output

 Number 56 divisible by 8
 Number 31 is not divisible by 8
 Number 32 divisible by 8
 Number 72 divisible by 8
 Number 78 is not divisible by 8
/*
    Java program for
    Number divisible by 8 using bitwise
*/
class Divisibility
{
    public void divisibleBy8(int num)
    {
        // Shift right by 3
        int auxiliary = num >> 3;
        // Shift left by 3
        auxiliary = auxiliary << 3;
        // Check if auxiliary is equal to number or not
        if (auxiliary == num)
        {
            System.out.print("\n Number " + num + " divisible by 8");
        }
        else
        {
            System.out.print("\n Number " + num + " is not divisible by 8");
        }
    }
    public static void main(String[] args)
    {
        Divisibility task = new Divisibility();
        // Test Inputs
        task.divisibleBy8(56);
        task.divisibleBy8(31);
        task.divisibleBy8(32);
        task.divisibleBy8(72);
        task.divisibleBy8(78);
    }
}

Output

 Number 56 divisible by 8
 Number 31 is not divisible by 8
 Number 32 divisible by 8
 Number 72 divisible by 8
 Number 78 is not divisible by 8
// Include header file
#include <iostream>
using namespace std;
/*
    C++ program for
    Number divisible by 8 using bitwise
*/
class Divisibility
{
    public: void divisibleBy8(int num)
    {
        // Shift right by 3
        int auxiliary = num >> 3;
        // Shift left by 3
        auxiliary = auxiliary << 3;
        // Check if auxiliary is equal to number or not
        if (auxiliary == num)
        {
            cout << "\n Number " << num << " divisible by 8";
        }
        else
        {
            cout << "\n Number " << num << " is not divisible by 8";
        }
    }
};
int main()
{
    Divisibility *task = new Divisibility();
    // Test Inputs
    task->divisibleBy8(56);
    task->divisibleBy8(31);
    task->divisibleBy8(32);
    task->divisibleBy8(72);
    task->divisibleBy8(78);
    return 0;
}

Output

 Number 56 divisible by 8
 Number 31 is not divisible by 8
 Number 32 divisible by 8
 Number 72 divisible by 8
 Number 78 is not divisible by 8
// Include namespace system
using System;
/*
    Csharp program for
    Number divisible by 8 using bitwise
*/
public class Divisibility
{
    public void divisibleBy8(int num)
    {
        // Shift right by 3
        int auxiliary = num >> 3;
        // Shift left by 3
        auxiliary = auxiliary << 3;
        // Check if auxiliary is equal to number or not
        if (auxiliary == num)
        {
            Console.Write("\n Number " + num + " divisible by 8");
        }
        else
        {
            Console.Write("\n Number " + num + " is not divisible by 8");
        }
    }
    public static void Main(String[] args)
    {
        Divisibility task = new Divisibility();
        // Test Inputs
        task.divisibleBy8(56);
        task.divisibleBy8(31);
        task.divisibleBy8(32);
        task.divisibleBy8(72);
        task.divisibleBy8(78);
    }
}

Output

 Number 56 divisible by 8
 Number 31 is not divisible by 8
 Number 32 divisible by 8
 Number 72 divisible by 8
 Number 78 is not divisible by 8
package main
import "fmt"
/*
    Go program for
    Number divisible by 8 using bitwise
*/

func divisibleBy8(num int) {
    // Shift right by 3
    var auxiliary int = num >> 3
    // Shift left by 3
    auxiliary = auxiliary << 3
    // Check if auxiliary is equal to number or not
    if auxiliary == num {
        fmt.Print("\n Number ", num, " divisible by 8")
    } else {
        fmt.Print("\n Number ", num, " is not divisible by 8")
    }
}
func main() {
    
    // Test Inputs
    divisibleBy8(56)
    divisibleBy8(31)
    divisibleBy8(32)
    divisibleBy8(72)
    divisibleBy8(78)
}

Output

 Number 56 divisible by 8
 Number 31 is not divisible by 8
 Number 32 divisible by 8
 Number 72 divisible by 8
 Number 78 is not divisible by 8
<?php
/*
    Php program for
    Number divisible by 8 using bitwise
*/
class Divisibility
{
    public  function divisibleBy8($num)
    {
        // Shift right by 3
        $auxiliary = $num >> 3;
        // Shift left by 3
        $auxiliary = $auxiliary << 3;
        // Check if auxiliary is equal to number or not
        if ($auxiliary == $num)
        {
            echo("\n Number ".$num.
                " divisible by 8");
        }
        else
        {
            echo("\n Number ".$num.
                " is not divisible by 8");
        }
    }
}

function main()
{
    $task = new Divisibility();
    // Test Inputs
    $task->divisibleBy8(56);
    $task->divisibleBy8(31);
    $task->divisibleBy8(32);
    $task->divisibleBy8(72);
    $task->divisibleBy8(78);
}
main();

Output

 Number 56 divisible by 8
 Number 31 is not divisible by 8
 Number 32 divisible by 8
 Number 72 divisible by 8
 Number 78 is not divisible by 8
/*
    Node JS program for
    Number divisible by 8 using bitwise
*/
class Divisibility
{
    divisibleBy8(num)
    {
        // Shift right by 3
        var auxiliary = num >> 3;
        // Shift left by 3
        auxiliary = auxiliary << 3;
        // Check if auxiliary is equal to number or not
        if (auxiliary == num)
        {
            process.stdout.write("\n Number " + num + " divisible by 8");
        }
        else
        {
            process.stdout.write("\n Number " + num + " is not divisible by 8");
        }
    }
}

function main()
{
    var task = new Divisibility();
    // Test Inputs
    task.divisibleBy8(56);
    task.divisibleBy8(31);
    task.divisibleBy8(32);
    task.divisibleBy8(72);
    task.divisibleBy8(78);
}
main();

Output

 Number 56 divisible by 8
 Number 31 is not divisible by 8
 Number 32 divisible by 8
 Number 72 divisible by 8
 Number 78 is not divisible by 8
#    Python 3 program for
#    Number divisible by 8 using bitwise
class Divisibility :
    def divisibleBy8(self, num) :
        #  Shift right by 3
        auxiliary = num >> 3
        #  Shift left by 3
        auxiliary = auxiliary << 3
        #  Check if auxiliary is equal to number or not
        if (auxiliary == num) :
            print("\n Number", num ,"divisible by 8", end = "")
        else :
            print("\n Number", num ,"is not divisible by 8", end = "")
        
    

def main() :
    task = Divisibility()
    #  Test Inputs
    task.divisibleBy8(56)
    task.divisibleBy8(31)
    task.divisibleBy8(32)
    task.divisibleBy8(72)
    task.divisibleBy8(78)

if __name__ == "__main__": main()

Output

 Number 56 divisible by 8
 Number 31 is not divisible by 8
 Number 32 divisible by 8
 Number 72 divisible by 8
 Number 78 is not divisible by 8
#    Ruby program for
#    Number divisible by 8 using bitwise
class Divisibility 
    def divisibleBy8(num) 
        #  Shift right by 3
        auxiliary = num >> 3
        #  Shift left by 3
        auxiliary = auxiliary << 3
        #  Check if auxiliary is equal to number or not
        if (auxiliary == num) 
            print("\n Number ", num ," divisible by 8")
        else
 
            print("\n Number ", num ," is not divisible by 8")
        end

    end

end

def main() 
    task = Divisibility.new()
    #  Test Inputs
    task.divisibleBy8(56)
    task.divisibleBy8(31)
    task.divisibleBy8(32)
    task.divisibleBy8(72)
    task.divisibleBy8(78)
end

main()

Output

 Number 56 divisible by 8
 Number 31 is not divisible by 8
 Number 32 divisible by 8
 Number 72 divisible by 8
 Number 78 is not divisible by 8
/*
    Scala program for
    Number divisible by 8 using bitwise
*/
class Divisibility()
{
    def divisibleBy8(num: Int): Unit = {
        // Shift right by 3
        var auxiliary: Int = num >> 3;
        // Shift left by 3
        auxiliary = auxiliary << 3;
        // Check if auxiliary is equal to number or not
        if (auxiliary == num)
        {
            print("\n Number " + num + " divisible by 8");
        }
        else
        {
            print("\n Number " + num + " is not divisible by 8");
        }
    }
}
object Main
{
    def main(args: Array[String]): Unit = {
        var task: Divisibility = new Divisibility();
        // Test Inputs
        task.divisibleBy8(56);
        task.divisibleBy8(31);
        task.divisibleBy8(32);
        task.divisibleBy8(72);
        task.divisibleBy8(78);
    }
}

Output

 Number 56 divisible by 8
 Number 31 is not divisible by 8
 Number 32 divisible by 8
 Number 72 divisible by 8
 Number 78 is not divisible by 8
/*
    Swift 4 program for
    Number divisible by 8 using bitwise
*/
class Divisibility
{
    func divisibleBy8(_ num: Int)
    {
        // Shift right by 3
        var auxiliary: Int = num >> 3;
        // Shift left by 3
        auxiliary = auxiliary << 3;
        // Check if auxiliary is equal to number or not
        if (auxiliary == num)
        {
            print("\n Number ", num ," divisible by 8", terminator: "");
        }
        else
        {
            print("\n Number ", num ," is not divisible by 8", terminator: "");
        }
    }
}
func main()
{
    let task: Divisibility = Divisibility();
    // Test Inputs
    task.divisibleBy8(56);
    task.divisibleBy8(31);
    task.divisibleBy8(32);
    task.divisibleBy8(72);
    task.divisibleBy8(78);
}
main();

Output

 Number  56  divisible by 8
 Number  31  is not divisible by 8
 Number  32  divisible by 8
 Number  72  divisible by 8
 Number  78  is not divisible by 8
/*
    Kotlin program for
    Number divisible by 8 using bitwise
*/
class Divisibility
{
    fun divisibleBy8(num: Int): Unit
    {
        // Shift right by 3
        var auxiliary: Int = num shr 3;
        // Shift left by 3
        auxiliary = auxiliary shl 3;
        // Check if auxiliary is equal to number or not
        if (auxiliary == num)
        {
            print("\n Number " + num + " divisible by 8");
        }
        else
        {
            print("\n Number " + num + " is not divisible by 8");
        }
    }
}
fun main(args: Array < String > ): Unit
{
    val task: Divisibility = Divisibility();
    // Test Inputs
    task.divisibleBy8(56);
    task.divisibleBy8(31);
    task.divisibleBy8(32);
    task.divisibleBy8(72);
    task.divisibleBy8(78);
}

Output

 Number 56 divisible by 8
 Number 31 is not divisible by 8
 Number 32 divisible by 8
 Number 72 divisible by 8
 Number 78 is not divisible by 8

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