All about Bit Manipulation
Bit Manipulation is a technique used in a variety of problems to get the solution in an optimized way. This technique is very effective from a Competitive Programming point of view. It is all about Bitwise Operators which directly works upon binary numbers or bits of numbers that help the implementation fast. Below are the Bitwise Operators that are used:
- Bitwise AND (&)
- Bitwise OR (|)
- Bitwise XOR (^)
- Bitwise NOT (!)
Learn more about Bitwise Operators in this article.
Below are some common bit operations that are frequently used in programming:
Bitwise Operations:
Below is the table to illustrate the result when the operation is performed using Bitwise Operators. Here 0s or 1s mean a sequence of 0 or 1 respectively.Operators Operations Result XOR X ^ 0s X XOR X ^ 1s ~X XOR X ^ X 0 AND X & 0s 0 AND X & 1s X AND X & X X OR X | 0s X OR X | 1s 1s OR X | X X
Get Bit:
This method is used to find the bit at a particular position(say i) of the given number N. The idea is to find the Bitwise AND of the given number and 2i that can be represented as (1 << i). If the value return is 1 then the bit at the ith position is set. Otherwise, it is unset.
Below is the pseudo-code for the same:
C++
// Function to get the bit at the // ith position boolean getBit( int num, int i) { // Return true if the bit is // set. Otherwise return false return ((num & (1 << i)) != 0); } |
Java
// Function to get the bit at the // ith position static boolean getBit( int num, int i) { // Return true if the bit is // set. Otherwise return false return ((num & ( 1 << i)) != 0 ); } // This code is contributed by rishavmahato348. |
Python3
# Function to get the bit at the # ith position def getBit(num, i): # Return true if the bit is # set. Otherwise return false return ((num & ( 1 << i)) ! = 0 ) # This code is contributed by shivani |
C#
// Function to get the bit at the // ith position static bool getBit( int num, int i) { // Return true if the bit is // set. Otherwise return false return ((num & (1 << i)) != 0); } // This code is contributed by subhammahato348. |
Javascript
<script> // Function to get the bit at the // ith position function getBit(num, i) { // Return true if the bit is // set. Otherwise return false return ((num & (1 << i)) != 0); } // This code is contributed by Ankita saini </script> |
Set Bit:
This method is used to set the bit at a particular position(say i) of the given number N. The idea is to update the value of the given number N to the Bitwise OR of the given number N and 2i that can be represented as (1 << i). If the value return is 1 then the bit at the ith position is set. Otherwise, it is unset.
Below is the pseudo-code for the same:
C++
// Function to set the ith bit of the // given number num int setBit( int num, int i) { // Sets the ith bit and return // the updated value return num | (1 << i); } |
Java
// Function to set the ith bit of the // given number num static int setBit( int num, int i) { // Sets the ith bit and return // the updated value return num | ( 1 << i); } // This code is contributed by subhammahato348 |
Python3
# Function to set the ith bit of the # given number num def setBit(num, i): # Sets the ith bit and return # the updated value return num | ( 1 << i) # This code is contributed by kirti |
C#
// Function to set the ith bit of the // given number num static int setBit( int num, int i) { // Sets the ith bit and return // the updated value return num | (1 << i); } |
Javascript
// Function to set the ith bit of the // given number num function setBit(num, i) { // Sets the ith bit and return // the updated value return num | (1 << i); } |
Clear Bit:
This method is used to clear the bit at a particular position(say i) of the given number N. The idea is to update the value of the given number N to the Bitwise AND of the given number N and the compliment of 2i that can be represented as ~(1 << i). If the value return is 1 then the bit at the ith position is set. Otherwise, it is unset.
Below is the pseudo-code for the same:
C++
// Function to clear the ith bit of // the given number N int clearBit( int num, int i) { // Create the mask for the ith // bit unset int mask = ~(1 << i); // Return the update value return num & mask; } |
Java
// Function to clear the ith bit of // the given number N static int clearBit( int num, int i) { // Create the mask for the ith // bit unset int mask = ~( 1 << i); // Return the update value return num & mask; } // This code is contributed by subham348 |
Python3
# Function to clear the ith bit of # the given number N def clearBit(num, i): # Create the mask for the ith # bit unset mask = ~( 1 << i) # Return the update value return num & mask # This code is contributed by subhammahato348 |
C#
// Function to clear the ith bit of // the given number N static int clearBit( int num, int i) { // Create the mask for the ith // bit unset int mask = ~(1 << i); // Return the update value return num & mask; } // This code is contributed by Ankita Saini |
Javascript
// Function to clear the ith bit of // the given number N function clearBit(num, i) { // Create the mask for the ith // bit unset let mask = ~(1 << i); // Return the update value return num & mask; } // This code is contributed by souravmahato348. |
Below is the program that implements the above functionalities:
C++
// C++ program to implement all the // above functionalities #include "bits/stdc++.h" using namespace std; // Function to get the bit at the // ith position bool getBit( int num, int i) { // Return true if the ith bit is // set. Otherwise return false return ((num & (1 << i)) != 0); } // Function to set the ith bit of the // given number num int setBit( int num, int i) { // Sets the ith bit and return // the updated value return num | (1 << i); } // Function to clear the ith bit of // the given number N int clearBit( int num, int i) { // Create the mask for the ith // bit unset int mask = ~(1 << i); // Return the update value return num & mask; } // Driver Code int main() { // Given number N int N = 70; cout << "The bit at the 3rd position from LSB is: " << (getBit(N, 3) ? '1' : '0' ) << endl; cout << "The value of the given number " << "after setting the bit at " << "LSB is: " << setBit(N, 0) << endl; cout << "The value of the given number " << "after clearing the bit at " << "LSB is: " << clearBit(N, 0) << endl; return 0; } |
Java
// Java program to implement all the // above functionalities import java.io.*; class GFG{ // Function to get the bit at the // ith position static boolean getBit( int num, int i) { // Return true if the ith bit is // set. Otherwise return false return ((num & ( 1 << i)) != 0 ); } // Function to set the ith bit of the // given number num static int setBit( int num, int i) { // Sets the ith bit and return // the updated value return num | ( 1 << i); } // Function to clear the ith bit of // the given number N static int clearBit( int num, int i) { // Create the mask for the ith // bit unset int mask = ~( 1 << i); // Return the update value return num & mask; } // Driver Code public static void main(String[] args) { // Given number N int N = 70 ; System.out.println( "The bit at the 3rd position from LSB is: " + (getBit(N, 3 ) ? '1' : '0' )); System.out.println( "The value of the given number " + "after setting the bit at " + "LSB is: " + setBit(N, 0 )); System.out.println( "The value of the given number " + "after clearing the bit at " + "LSB is: " + clearBit(N, 0 )); } } // This code is contributed by souravmahato348 |
Python
# Python program to implement all the # above functionalities # Function to get the bit at the # ith position def getBit( num, i): # Return true if the ith bit is # set. Otherwise return false return ((num & ( 1 << i)) ! = 0 ) # Function to set the ith bit of the # given number num def setBit( num, i): # Sets the ith bit and return # the updated value return num | ( 1 << i) # Function to clear the ith bit of # the given number N def clearBit( num, i): # Create the mask for the ith # bit unset mask = ~( 1 << i) # Return the update value return num & mask # Driver Code # Given number N N = 70 print "The bit at the 3rd position from LSB is: " , 1 if (getBit(N, 3 )) else '0' print "The value of the given number" , "after setting the bit at" , "LSB is: " , setBit(N, 0 ) print "The value of the given number" , "after clearing the bit at" , "LSB is: " , clearBit(N, 0 ) # This code is contributed by shivanisinghss2110 |
C#
// C# program to implement all the // above functionalities using System; class GFG { // Function to get the bit at the // ith position static bool getBit( int num, int i) { // Return true if the ith bit is // set. Otherwise return false return ((num & (1 << i)) != 0); } // Function to set the ith bit of the // given number num static int setBit( int num, int i) { // Sets the ith bit and return // the updated value return num | (1 << i); } // Function to clear the ith bit of // the given number N static int clearBit( int num, int i) { // Create the mask for the ith // bit unset int mask = ~(1 << i); // Return the update value return num & mask; } // Driver Code public static void Main() { // Given number N int N = 70; Console.WriteLine( "The bit at the 3rd position form LSB is: " + (getBit(N, 3) ? '1' : '0' )); Console.WriteLine( "The value of the given number " + "after setting the bit at " + "LSB is: " + setBit(N, 0)); Console.WriteLine( "The value of the given number " + "after clearing the bit at " + "LSB is: " + clearBit(N, 0)); } } // This code is contributed by rishavmahato348. |
Javascript
<script> // Javascript program to implement all // the above functionalities // Function to get the bit at the // ith position function getBit(num, i) { // Return true if the ith bit is // set. Otherwise return false return ((num & (1 << i)) != 0); } // Function to set the ith bit of the // given number num function setBit(num, i) { // Sets the ith bit and return // the updated value return num | (1 << i); } // Function to clear the ith bit of // the given number N function clearBit(num, i) { // Create the mask for the ith // bit unset let mask = ~(1 << i); // Return the update value return num & mask; } // Driver code // Given number N let N = 70; document.write( "The bit at the 3rd position from LSB is: " + (getBit(N, 3) ? '1' : '0' ) + "</br>" ); document.write( "The value of the given number " + "after setting the bit at " + "LSB is: " + setBit(N, 0) + "</br>" ); document.write( "The value of the given number " + "after clearing the bit at " + "LSB is: " + clearBit(N, 0) + "</br>" ); // This code is contributed by divyeshrabadiya07 </script> |
The bit at the 3rd position is: 0 The value of the given number after setting the bit at MSB is: 71 The value of the given number after clearing the bit at MSB is: 70