Set all even bits of a number
Last Updated :
21 Nov, 2022
Given a number, the task is to set all even bits of a number. Positions of bits are counted from LSB (least significant bit) to MSB (Most significant bit). The position of LSB is considered as 1.
Examples :
Input : 20
Output : 30
Binary representation of 20 is
10100. After setting
even bits, we get 11110
Input : 10
Output : 10
Method 1:
- First, generate a number that contains even position bits.
- Take OR with the original number. Note that 1 | 1 = 1 and 1 | 0 = 1.
Let’s understand this approach with the below code.
C++
// Simple CPP program to set all even
// bits of a number
#include <iostream>
using namespace std;
// Sets even bits of n and returns
// modified number.
int evenbitsetnumber(int n)
{
// Generate 101010...10 number and
// store in res.
int count = 0, res = 0;
for (int temp = n; temp > 0; temp >>= 1) {
// if bit is even then generate
// number and or with res
if (count % 2 == 1)
res |= (1 << count);
count++;
}
// return OR number
return (n | res);
}
int main()
{
int n = 10;
cout << evenbitsetnumber(n);
return 0;
}
// Simple Java program to set all even
// bits of a number
class GFG
{
// Sets even bits of n and returns
// modified number.
static int evenbitsetnumber(int n)
{
// Generate 101010...10 number and
// store in res.
int count = 0, res = 0;
for (int temp = n; temp > 0; temp >>= 1) {
// if bit is even then generate
// number and or with res
if (count % 2 == 1)
res |= (1 << count);
count++;
}
// return OR number
return (n | res);
}
// Driver code
public static void main(String[] args)
{
int n = 4;
System.out.println(evenbitsetnumber(n));
}
}
// This code is contributed
// by prerna saini.
# Simple Python program to set all even
# bits of a number
# Sets even bits of n and returns
# modified number.
def evenbitsetnumber(n):
# Generate 101010...10 number and
# store in res.
count = 0
res = 0
temp = n
while(temp > 0):
# if bit is even then generate
# number and or with res
if (count % 2 == 1):
res |= (1 << count)
count+=1
temp >>= 1
# return OR number
return (n | res)
n = 10
print(evenbitsetnumber(n))
# This code is contributed
# by Smitha Dinesh Semwal
// Simple C# program to set
// all even bits of a number
using System;
class GFG
{
// Sets even bits of n and
// returns modified number.
static int evenbitsetnumber(int n) {
// Generate 101010...10 number
// and store in res.
int count = 0, res = 0;
for (int temp = n; temp > 0; temp >>= 1) {
// if bit is even then generate
// number and or with res
if (count % 2 == 1)
res |= (1 << count);
count++;
}
// return OR number
return (n | res);
}
// Driver code
public static void Main()
{
int n = 4;
Console.WriteLine(evenbitsetnumber(n));
}
}
// This code is contributed by vt_m.
<?php
// Simple php program to set
// all even bits of a number
// Sets even bits of n and
// returns modified number.
function evenbitsetnumber($n)
{
// Generate 101010...10 number
// and store in res.
$count = 0;
$res = 0;
for ($temp = $n; $temp > 0; $temp >>= 1)
{
// if bit is even then generate
// number and or with res
if ($count % 2 == 1)
$res |= (1 << $count);
$count++;
}
// return OR number
return ($n | $res);
}
//Driver Code
$n = 10;
echo evenbitsetnumber($n);
//This Code is contributed by mits
?>
<script>
// JavaScript program to set all even
// bits of a number
// Sets even bits of n and returns
// modified number.
function evenbitsetnumber(n)
{
// Generate 101010...10 number and
// store in res.
let count = 0, res = 0;
for(let temp = n; temp > 0; temp >>= 1)
{
// If bit is even then generate
// number and or with res
if (count % 2 == 1)
res |= (1 << count);
count++;
}
// Return OR number
return (n | res);
}
// Driver Code
let n = 10;
document.write(evenbitsetnumber(n));
// This code is contributed by avijitmondal1998
</script>
Method 2 (A O(1) solution for 32 bit numbers)
C++
// Efficient CPP program to set all even
// bits of a number
#include <iostream>
using namespace std;
// return msb set number
int getmsb(int n)
{
// set all bits
n |= n >> 1;
n |= n >> 2;
n |= n >> 4;
n |= n >> 8;
n |= n >> 16;
// return msb
// increment n by 1
// and shift by 1
return (n + 1) >> 1;
}
// return even set number
int getevenbits(int n)
{
// get msb here
n = getmsb(n);
// generate even bits like 101010..
n |= n >> 2;
n |= n >> 4;
n |= n >> 8;
n |= n >> 16;
// if bits is odd then shift by 1
if (n & 1)
n = n >> 1;
// return even set bits number
return n;
}
// set all even bits here
int setallevenbits(int n)
{
// take or with even set bits number
return n | getevenbits(n);
}
int main()
{
int n = 10;
cout << setallevenbits(n);
return 0;
}
// Efficient Java program to
// set all even bits of a number
import java.io.*;
class GFG
{
// return msb set number
static int getmsb(int n)
{
// set all bits
n |= n >> 1;
n |= n >> 2;
n |= n >> 4;
n |= n >> 8;
n |= n >> 16;
// return msb
// increment n by 1
// and shift by 1
return (n + 1) >> 1;
}
// return even set number
static int getevenbits(int n)
{
// get msb here
n = getmsb(n);
// generate even
// bits like 101010..
n |= n >> 2;
n |= n >> 4;
n |= n >> 8;
n |= n >> 16;
// if bits is odd
// then shift by 1
if ((n & 1) == 1)
n = n >> 1;
// return even
// set bits number
return n;
}
// set all even bits here
static int setallevenbits(int n)
{
// take or with even
// set bits number
return n | getevenbits(n);
}
// Driver Code
public static void main (String[] args)
{
int n = 10;
System.out.println(setallevenbits(n));
}
}
// This code is contributed by ajit
# Efficient Python 3
# program to set all even
# bits of a number
# return msb set number
def getmsb(n):
# set all bits
n |= n >> 1
n |= n >> 2
n |= n >> 4
n |= n >> 8
n |= n >> 16
# return msb
# increment n by 1
# and shift by 1
return (n + 1) >> 1
# return even set number
def getevenbits(n):
# get msb here
n = getmsb(n)
# generate even bits like 101010..
n |= n >> 2
n |= n >> 4
n |= n >> 8
n |= n >> 16
# if bits is odd then shift by 1
if (n & 1):
n = n >> 1
# return even set bits number
return n
# set all even bits here
def setallevenbits(n):
# take or with even set bits number
return n | getevenbits(n)
n = 10
print(setallevenbits(n))
# This code is contributed by
# Smitha Dinesh Semwal
// Efficient C# program to
// set all even bits of a number
using System;
class GFG
{
// return msb set number
static int getmsb(int n)
{
// set all bits
n |= n >> 1;
n |= n >> 2;
n |= n >> 4;
n |= n >> 8;
n |= n >> 16;
// return msb
// increment n by 1
// and shift by 1
return (n + 1) >> 1;
}
// return even set number
static int getevenbits(int n)
{
// get msb here
n = getmsb(n);
// generate even
// bits like 101010..
n |= n >> 2;
n |= n >> 4;
n |= n >> 8;
n |= n >> 16;
// if bits is odd
// then shift by 1
if ((n & 1) == 1)
n = n >> 1;
// return even
// set bits number
return n;
}
// set all even bits here
static int setallevenbits(int n)
{
// take or with even
// set bits number
return n | getevenbits(n);
}
// Driver Code
public static void Main ()
{
int n = 10;
Console.WriteLine(setallevenbits(n));
}
}
// This code is contributed by aj_36
<?php
// Efficient php program to set
// all even bits of a number
// return msb set number
function getmsb($n)
{
// set all bits
$n |= $n >> 1;
$n |= $n >> 2;
$n |= $n >> 4;
$n |= $n >> 8;
$n |= $n >> 16;
// return msb
// increment n by 1
// and shift by 1
return ($n + 1) >> 1;
}
// return even set number
function getevenbits($n)
{
// get msb here
$n = getmsb($n);
// generate even bits
// like 101010..
$n |= $n >> 2;
$n |= $n >> 4;
$n |= $n >> 8;
$n |= $n >> 16;
// if bits is odd then
// shift by 1
if ($n & 1)
$n = $n >> 1;
// return even set
// bits number
return $n;
}
// set all even bits here
function setallevenbits($n)
{
// take or with even
// set bits number
return $n | getevenbits($n);
}
//Driver code
$n = 10;
echo setallevenbits($n);
//This code is contributed by mits
?>
<script>
// Efficient Javascript program to
// set all even bits of a number
// Return msb set number
function getmsb(n)
{
// Set all bits
n |= n >> 1;
n |= n >> 2;
n |= n >> 4;
n |= n >> 8;
n |= n >> 16;
// Return msb
// increment n by 1
// and shift by 1
return (n + 1) >> 1;
}
// Return even set number
function getevenbits(n)
{
// Get msb here
n = getmsb(n);
// Generate even
// bits like 101010..
n |= n >> 2;
n |= n >> 4;
n |= n >> 8;
n |= n >> 16;
// If bits is odd
// then shift by 1
if ((n & 1) == 1)
n = n >> 1;
// Return even
// set bits number
return n;
}
// Set all even bits here
function setallevenbits(n)
{
// Take or with even
// set bits number
return n | getevenbits(n);
}
// Driver code
let n = 10;
document.write(setallevenbits(n));
// This code is contributed by decode2207
</script>
Method 3: Using bit mask
To set a bit, we can take OR of 1 and that bit (as 1 | 1 = 1, and 1 | 0 = 1). Therefore, to set all odd bits of an n-bit number, we need to use a bit mask which is an n-bit binary number with all odd bits set. This mask can be generated in 1 step using the formula of sum of a geometric progression, as an n bit number ...1010 is equal to 21 + 23 + 25 + .... 2 (n - !(n % 1)) .
Approach:
- Calculate the number of bits using log2(number)
- Calculate the largest power m, of the GP series using the formula (numOfBits - !(numOfBits % 1)).
- Calculate the value of the mask using the formula: a × (r m + 1 - 1) / (r - 1).
- Perform the setting operation using number | mask.
C++
// Simple CPP program to set all even
// bits of a number
#include <bits/stdc++.h>
using namespace std;
//function to set all the even bits
long long int setEvenBits(long long int n) {
//calculating number of bits using log
int numOfBits = 1 + (int)log2(n);
//if there is only one bit,
if (numOfBits == 1)
return n;
//calculating the max power of GP series
int m = (numOfBits - !(numOfBits % 1)) / 2 ;
//calculating mask using GP sum
//which is a(r ^ n - 1) / (r - 1)
//where a = 2, r = 4, n = m
int mask = (2 * ((1 << (2 * m)) - 1)) / 3;
//toggling all even bits using mask | n
return mask | n;
}
//Driver Code
int main()
{
int n = 102121;
cout << setEvenBits(n);
return 0;
}
//This approach is contributed by phasing17
// Simple Java program to set all even
// bits of a number
import java.util.*;
class GFG {
// function to set all the even bits
static int setEvenBits(int n)
{
// calculating number of bits using log
int numOfBits
= 1 + (int)(Math.log(n) / Math.log(2));
// if there is only one bit,
if (numOfBits == 1)
return n;
// calculating the max power of GP series
int m = (numOfBits - 1 ^ (numOfBits % 1)) / 2;
// calculating mask using GP sum
// which is a(r ^ n - 1) / (r - 1)
// where a = 2, r = 4, n = m
int mask = (2 * ((1 << (2 * m)) - 1)) / 3;
// toggling all even bits using mask | n
return mask | n;
}
// Driver Code
public static void main(String[] args)
{
int n = 102121;
System.out.println(setEvenBits(n));
}
}
// This code is contributed by phasing17
# Simple Python3 program to set all even
# bits of a number
from math import log
# function to set all the even bits
def setEvenBits(n):
# calculating number of bits using log
numOfBits = 1 + int(log(n, 2))
# if there is only one bit,
if numOfBits == 1:
return n
# calculating the max power of GP series
m = int((numOfBits - 1 ^ (numOfBits % 1)) / 2)
# calculating mask using GP sum
# which is a(r ^ n - 1) / (r - 1)
# where a = 2, r = 4, n = m
mask = int((2 * ((1 << (2 * m)) - 1)) / 3)
# toggling all even bits using mask | n
return mask | n
# Driver Code
n = 102121
print(setEvenBits(n))
# This code is contributed by phasing17
// Simple C# program to set all even
// bits of a number
using System;
class GFG
{
// function to set all the even bits
static int setEvenBits(int n)
{
// calculating number of bits using log
int numOfBits
= 1 + (int)(Math.Log(n) / Math.Log(2));
// if there is only one bit,
if (numOfBits == 1)
return n;
// calculating the max power of GP series
int m = (numOfBits - 1 ^ (numOfBits % 1)) / 2;
// calculating mask using GP sum
// which is a(r ^ n - 1) / (r - 1)
// where a = 2, r = 4, n = m
int mask = (2 * ((1 << (2 * m)) - 1)) / 3;
// toggling all even bits using mask | n
return mask | n;
}
// Driver Code
public static void Main(string[] args)
{
int n = 102121;
Console.WriteLine(setEvenBits(n));
}
}
// This code is contributed by phasing17
// Simple JavaScript program to set all even
// bits of a number
// function to set all the even bits
function setEvenBits(n) {
// calculating number of bits using log
let numOfBits = 1 + Math.floor(Math.log2(n));
// if there is only one bit,
if (numOfBits == 1)
return n;
// calculating the max power of GP series
let m = Math.floor((numOfBits - !(numOfBits % 1)) / 2);
// calculating mask using GP sum
// which is a(r ^ n - 1) / (r - 1)
// where a = 2, r = 4, n = m
let mask = Math.floor((2 * ((1 << (2 * m)) - 1)) / 3);
// toggling all even bits using mask | n
return mask | n;
}
// Driver Code
let n = 102121;
console.log(setEvenBits(n));
// This approach is contributed by phasing17
Time Complexity: O(1)
Auxiliary Space: O(1)
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