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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;

1. What will be the output of the pseudo-code for the input $x = 13$?
2. What will be the output of the pseudo-code for an arbitrary non-negative integer $x < 2^{32}$?
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(i) 3

(ii) Highest power of 2

(i) 3

(ii) For non negative integers, it counts the number of 1s in the binary representation of the number. Ex: x=13 (1101) will give 3

Edit: It seems this question was also asked in TIFR 2014. (https://gateoverflow.in/27136/tifr2014-b-2?show=27160)

by Junior (943 points)
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