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In a two's complement number system, `x &= (x-1)`

deletes the rightmost 1-bit in
`x`

. Explain why. Use this observation to write a faster version of `bitcount`

.

```
#include <limits.h>
#include <stdio.h>
/* Subtracting 1 from a binary number has the effect of inverting all the bits up to and
* including the first 1-bit. ANDing the inverted with the original will ensure all bits
* up to the first 1-bit are 0. */
int bitcount(unsigned x);
int main()
{
printf("%d\n", bitcount(0b000));
}
int bitcount(unsigned x)
{
int count = 0;
while (x &= (x - 1)) {
count++;
}
return count ? count + 1 : count;
}
```