How to Apply Binary Transformations?
This is a one-off trick which is not part of a complete methodology. To see why the trick works, suppose that the index has the form $x10^m$. To calculate its two's complement, we first complement it to $\bar{x}01^m$, then add 1 to get $\bar{x}10^m$. ANDing the index and its two's complement, we get $0^{|x|}10^m$. Subtracting this from the index, we get $x0^{m+1}$, as needed.