Explanation needed

#1

Unable to get the logic .
Can you explain with the help of an example

#2

Which question are you referring to? Please mention .

#3

Question no.- 4

Which one line function can be used to get index of the least significant bit that is on (first 1 from right to left in binary representation of an integer) ?

#4

The answer should be log2( N & -N ) + 1 , if n is a positive number , so -n will be a negative number and negative number are represented in 2’s compliment ,which is ~n+1 , ~n has all the bits of n inverted due to which we get 0 in place of 1 and vice versa so when we add 1 to ~n then that 1 occupies the first rightmost 0 in (~n)(which is same as rightmost 1 value in n) and other bits have inverted values or zero values . so when we perform & operation we get only rightmost bit set in the function ,and then we perform logn (base2) to get corresponding index.

eg :- n = 1110010100
~n= 0001101011
~n+1=-n= 0001101100
(n&(-n))= 0000000100 = 4
log(4) =2
2+1=3 which is the answer

you should try applying the formula on some examples on your own for better clarity