Question

Write code to implement the following function:
/* * Generate mask indicating leftmost 1 in x. Assume w=32. * For example 0xFF00 -> 0x8000, and 0x6600 --> 0x4000. * If x = 0,then return 0. */
int leftmost_one(unsigned x);

Your function should follow the above bit-level integer coding rules, except that you may assume that data type int has w=32 bits. Your code should contain a total of at most 15 arithmetic, bit-wise, and logical operations.

In C++ and has to obey following rules

Write the required code expressions in separate functions. Write the required functions and test with a small main program. All programs should be tested and the output should be pasted below the main program.

Your code must follow these rules:

Assumptions • Integers are represented in two’s-complement form. • Right shifts of signed data are performed arithmetically. • Datatype int is w bits long. For some of the problems, you will be given a specific value for w, but otherwise your code should work as long as w is a multiple of 8. You can use the expression sizeof(int)<<3 to compute w.

Forbidden • Conditionals (if or ? :), loops, switch statements, function calls, and macro invocations. • Division, modulus, and multiplication. • Relative comparison operators (<, >, <=, and >=)

Answer 1

#include <stdio.h>

int leftmost_one(unsigned x)

{

if(x == 0)

return 0;

// extending the leftmost one to the right end

x = x | (x >> 1);

x = x | (x >> 2);

x = x | (x >> 4);

x = x | (x >> 8);

x = x | (x >> 16);

// then subtract off all the other ones to get the resultant mask

int result = x - (x >> 1);

return result;

}

int main()

{

unsigned x;

printf("Enter x: ");

scanf("%i",&x);

printf("%i\n", leftmost_one(x));

return 0;

}

/*output:

Enter x: 0xFF00

32768

Enter x: 0x6600

16384

*/