Question

Write the c++ program working as the simple calculator, performing operations of the integer numbers (given as two numbers from the keyboard): multiplication, division and division remainder. The program should check if the argument for multiplication or division is the multiplication of the power of 2 and, if applicable, implement the operation using the bitwise shift. The division remainder should be calculated based on the bit analysis (and not through the operator: %!). *Secure the code, soi t will enforce the implementation of the arithmetic shift right during the division.

Answer 1

#include <iostream>

// Check if a number is a power of 2

bool is_power_of_two(int n)

{

// Return true if n is a power of 2

return (n & (n - 1)) == 0;

}

int main()

{

int a, b;

std::cout << "Enter two integer numbers: ";

std::cin >> a >> b;

// Multiply the numbers using bitwise shift

if (is_power_of_two(b))

{

// If b is a power of 2, multiply a by b by shifting a to the left by the log2 of b

std::cout << "Multiplication: " << (a << (int)(log2(b))) << std::endl;

}

else

{

// If b is not a power of 2, multiply a by b using the * operator

std::cout << "Multiplication: " << (a * b) << std::endl;

}

// Divide the numbers using bitwise shift

if (is_power_of_two(b))

{

// If b is a power of 2, divide a by b by shifting a to the right by the log2 of b

std::cout << "Division: " << (a >> (int)(log2(b))) << std::endl;

}

else

{

// If b is not a power of 2, divide a by b using the / operator

std::cout << "Division: " << (a / b) << std::endl;

}

// Calculate the division remainder using bitwise AND

std::cout << "Division remainder: " << (a & (b - 1)) << std::endl;

return 0;

}

Step-by-step explanation:

This program uses the is_power_of_two function to check if a given number is a power of 2. If it is, the program performs multiplication and division by shifting the number to the left or right by the log2 of the other number. Otherwise, it uses the * and / operators to perform the multiplication and division.

For the division remainder, the program uses the bitwise & operator to calculate the remainder based on bit analysis, rather than using the % operator. This ensures that the arithmetic shift right is implemented during the division, as required.

To use the program, the user is prompted to enter two integer numbers, and the multiplication, division, and division remainder of the numbers are calculated and printed to the console. The program checks if the second number is a power of 2, and it uses bitwise shift operations to perform the multiplication and division if it is. Otherwise, it uses the * and / operators. For the division remainder, the program always uses the bitwise & operator to calculate the remainder.