Let $x, y$ be two non-negative integers $< 2^{32}$. By $x \wedge y$ we mean the integer represented by the bitwise logical $AND$ of the 32- bit binary representations of $x$ and $y$. For example, if $x = 13$ and $y = 6$, then $x \wedge y$ is the bitwise $AND$ of 0$^{28}$1101 and 0$^{28}$0110, resulting in 0$^{28}$0100, which is 4 in decimal. (Here 0$^{28}$1101 means twenty-eight 0’s followed by the 4-bit string 1101.) Now consider the following pseudo-code:
integer x, n = 0;
while (x $\neq$ 0){
x $\leftarrow$ x $\wedge$ (x − 1);
n $\leftarrow$ n + 1;
}
print n;
- What will be the output of the pseudo-code for the input $x = 13$?
- What will be the output of the pseudo-code for an arbitrary non-negative integer $x < 2^{32}$?
