added bitwise operators

README.md

@@ -5,7 +5,8 @@ This repository contains notes and starter code for Bit manipulation and mathema
 ## Topics to be covered :
 
 View the list at -> https://docs.google.com/document/d/1W0GUTM3uBY2wt5pu1eRxmHKytSndcFpVoxdujh0gdhs/edit?usp=sharing
-Bit manipulation -
+
+### Bit manipulation -
 
 1. Converting a number to binary
 2. Bitwise operators introduction
@@ -14,7 +15,7 @@ Bit manipulation -
 5. Find the number occuring odd number of times
 6. Position of first right bit
 
-Mathematics -
+#### Mathematics -
 
 1. Euclidean algorithm (GCD)
 2. LCM

bitmanipulation.cpp

@@ -1,20 +1,36 @@
 #include<bits/stdc++.h>
 using namespace std;
 int main(){
-    // count set bits in every number from 1 to n
-    // brian kernighan algortihm
-    // n = 10 -> 1010 -> 2 set bits
-    // n-1 = 9 -> 1001
-    // n-1 = 8 -> 1000
-    //  n= 16 -> 10000
-    // n-1 -> 01111 -> 15
-    // n-1 -> 14  -> 01110
-    // 10&9 -> 1000 -> 1 set bit
-    // n=n&(n-1) -> 8&7 -> 0000 > 0 set bit
-    // n&(n-1) -> it loses one rightmost bit at a time
-    while(n){
-        n = n&(n-1);
-        count++;
+    int n = 10;
+    // 168421
+    // 16+1 -> 10001
+    // 10-> 1010
+    int binary[10];
+    int i = 0;
+    // n = 10
+    while(n>0){
+        // binary[0] = 0
+        // binary[1] = 1
+        // binary[2] = 0
+        // binary[3]= 1
+        // 0101
+        binary[i] = n%2;
+        // 10-> 5
+        // 5/2 -> 2
+        n=n/2;
+        // i=1
+        // i=2
+        i++;
+    }
+    // 17/2 -> 1
+    // 8/2 -> 0
+    // 4/2 ->0
+    // 2/2-> 0
+    // 1/2 -> 1
+
+    // dry run for 10 
+    for(int k = i-1;k>=0;k--){
+        cout<<binary[k];
     }
     return 0;
 }

bitwise.cpp

@@ -0,0 +1,28 @@
+#include<bits/stdc++.h>
+using namespace std;
+int main(){
+    cout<<sizeof(int)<<endl;
+    // 4 bytes -> 32 bits
+    // a-> 0101 
+    int a = 5;
+    // b-> 1001
+    int b = 9;
+    // 6 bitwise operators
+    // a&b -> 0001 ->1
+    cout<<(a&b)<<endl;
+    // a|b-> 1101 ->13
+    cout<<(a|b)<<endl;
+    // 1100 -> 12
+    cout<<(a^b)<<endl;
+    // 01001 -> 10010 -> 18
+    cout<<(b<<1)<<endl;
+    // 1001-> 0100 -> 4
+    cout<<(b>>1)<<endl;
+    // a -> 0(28).....0101 -> 1(28)...1010 -> 8+2 = 10
+    // whenever there is a 1 present at the first index -> it is a negative number
+    // 2s complement = 1s complement + 1
+    // 0(28)...0101 = 0101+1 = 0110 -> 6
+    // -6
+    cout<<(~a)<<endl;
+
+}