Please solve this question:

Write a Java function that performs the functionality of the headers below. String leftmost_one (int x)

Namely, the leftmost_one method should return a mask indicating the leftmost 1 in the input number x.

For example:

Input Output

0xFF00 0x8000

0x6600 0x4000

Moreover, you must implement this function using only straightline code (i.e., no loops or conditionals1 ) and a limited number of arithmetic and logical operators. Specifically, you are only allowed to use the following operators: , &, >>, >>, |,

Your code should contain a total of at most 15 arithmetic, bitwise, and logical operations. To return your solution as a String with hexadecimal format, you should use the in-built Java function:

String.format( 0x%08X, z),

where z is a int variable. For instance, System.out.println( String.format( 0x%08X, 65280) prints 0x0000FF00.

Hint: First transform x into a bit vector of the form [0 . . . 011111], where you turn any bit to right of the left most as 1. Then, think about how you can vanish all the 1s but the leftmost one.

Evaluation: This question is worth 18 marks. You will receive 3 marks (per function) simply for each of the following test cases:

Test case Input Input in hexadecimal Output

1 65,280 0x0000FF00 0x00008000

2 26,112 0x00006600 0x00004000

3 -680 0xFFFFFD58 0x80000000

4 0 0x00000000 0x00000000

5 2,147,483,647 0x7FFFFFFF 0x40000000

6 -2,147,483,648 0x80000000 0x8000000