Currently studing bit-manipulation and like to share some interesting catch that i got.

1. As last bit for a give number n is (n&1), but we can also got this value through ((n)&(-n)).

2. If we have given two numbers a and b, and ask to count number of bit change in a to conver a to b, is simply count 1's set bit in (a^b), where ^ is xor operator.

3. Best way to count 1's set bit for any nuber n by using n=(n&(n-1);

   while(n) { n=n&(n-1); count_setbit++; //Count 1's set bit. }

4. Programme to generate all possible subsequence of a given string

   #include <bits/stdc++.h>
           using namespace std;
           int main()
           {
               string s;   cin>>s;
   
               int len=s.size();
   
               for(int i=0;i<1<<len;i++)
               {
                   int n=i;    string ans="";
   
                   for(int j=0;j<len;j++)
                   if(n&(1<<j))
                   ans+=s[j];
                   cout<<ans<<"\n";
               } 
               return 0;
           }

I'm parise if you share more initiation like this.