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All about Bit Manipulation
  • Last Updated : 13 May, 2021

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 means sequence of 0 or 1 respectively.

OperatorsOperationsResult
XORX ^ 0sX
XORX ^ 1s~X
XORX ^ X0
ANDX & 0s0
ANDX & 1sX
ANDX & XX
ORX | 0sX
ORX | 1s1s
ORX | XX

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.

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.

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

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);
}

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;
}

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 is: "
         << (getBit(N, 3) ? '1' : '0')
         << endl;
 
    cout << "The value of the given number "
         << " after setting the bit at "
         << " MSB is: "
         << setBit(N, 0) << endl;
 
    cout << "The value of the given number "
         << " after clearing the bit at "
         << " MSB is: "
         << clearBit(N, 0) << endl;
 
    return 0;
}
Output: 
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

 

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