# Inserting m into n such that m starts at bit j and ends at bit i.

We are given two numbers n and m, and two-bit positions, i and j. Insert bits of m into n starting from j to i. We can assume that the bits j through i have enough space to fit all of m. That is, if m = 10011, you can assume that there are at least 5 bits between j and i. You would not, for example, have j = 3 and i = 2, because m could not fully fit between bit 3 and bit 2. **Examples :**

Input : n = 1024 m = 19 i = 2 j = 6; Output : n = 1100 Binary representations of input numbers m in binary is (10011)_{2}n in binary is (10000000000)_{2}Binary representations of output number (10000000000)_{2}Input : n = 5 m = 3 i = 1 j = 2 Output : 7

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**Algorithm :**

1. Clear the bits j through i in n 2. Shift m so that it lines up with bits j through i 3. Return Bitwise AND of m and n.

The trickiest part is Step 1. How do we clear the bits in n? We can do this with a mask. This mask will have all 1s, except for 0s in the bits j through i. We create this mask by creating the left half of the mask first, and then the right half.

Following is the implementation of the above approach.

## C++

`// C++ program for implementation of updateBits()` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// Function to updateBits M insert to N.` `int` `updateBits(` `int` `n, ` `int` `m, ` `int` `i, ` `int` `j)` `{` ` ` `/* Create a mask to clear bits i through j` ` ` `in n. EXAMPLE: i = 2, j = 4. Result` ` ` `should be 11100011. For simplicity, we'll` ` ` `use just 8 bits for the example. */` ` ` `int` `allOnes = ~0; ` `// will equal sequence of all ls` ` ` `// ls before position j, then 0s. left = 11100000` ` ` `int` `left= allOnes << (j + 1);` ` ` `// l's after position i. right = 00000011` ` ` `int` `right = ((1 << i) - 1);` ` ` `// All ls, except for 0s between i and j. mask 11100011` ` ` `int` `mask = left | right;` ` ` `/* Clear bits j through i then put min there */` ` ` `int` `n_cleared = n & mask; ` `// Clear bits j through i.` ` ` `int` `m_shifted = m << i; ` `// Move m into correct position.` ` ` `return` `(n_cleared | m_shifted); ` `// OR them, and we're done!` `}` `// Driver Code` `int` `main()` `{` ` ` `int` `n = 1024; ` `// in Binary N= 10000000000` ` ` `int` `m = 19; ` `// in Binary M= 10011` ` ` `int` `i = 2, j = 6;` ` ` `cout << updateBits(n,m,i,j);` ` ` `return` `0;` `}` |

## Java

`// Java program for implementation of updateBits()` `class` `UpdateBits` `{` ` ` `// Function to updateBits M insert to N.` ` ` `static` `int` `updateBits(` `int` `n, ` `int` `m, ` `int` `i, ` `int` `j)` ` ` `{` ` ` `/* Create a mask to clear bits i through j` ` ` `in n. EXAMPLE: i = 2, j = 4. Result` ` ` `should be 11100011. For simplicity, we'll` ` ` `use just 8 bits for the example. */` ` ` ` ` `int` `allOnes = ~` `0` `; ` `// will equal sequence of all ls` ` ` ` ` `// ls before position j, then 0s. left = 11100000` ` ` `int` `left= allOnes << (j + ` `1` `);` ` ` ` ` `// l's after position i. right = 00000011` ` ` `int` `right = ((` `1` `<< i) - ` `1` `);` ` ` ` ` `// All ls, except for 0s between i and j. mask 11100011` ` ` `int` `mask = left | right;` ` ` ` ` `/* Clear bits j through i then put min there */` ` ` `// Clear bits j through i.` ` ` `int` `n_cleared = n & mask;` ` ` `// Move m into correct position.` ` ` `int` `m_shifted = m << i; ` ` ` ` ` `// OR them, and we're done!` ` ` `return` `(n_cleared | m_shifted);` ` ` `}` ` ` ` ` `public` `static` `void` `main (String[] args)` ` ` `{` ` ` `// in Binary N= 10000000000` ` ` `int` `n = ` `1024` `;` ` ` ` ` `// in Binary M= 10011` ` ` `int` `m = ` `19` `; ` ` ` ` ` `int` `i = ` `2` `, j = ` `6` `;` ` ` ` ` `System.out.println(updateBits(n,m,i,j));` ` ` `}` `}` |

## Python3

`# Python3 program for implementation` `# of updateBits()` `# Function to updateBits M insert to N.` `def` `updateBits(n, m, i, j):` ` ` `# Create a mask to clear bits i through` ` ` `# j in n. EXAMPLE: i = 2, j = 4. Result` ` ` `# should be 11100011. For simplicity,` ` ` `# we'll use just 8 bits for the example.` ` ` `# will equal sequence of all ls` ` ` `allOnes ` `=` `~` `0` ` ` `# ls before position j,` ` ` `# then 0s. left = 11100000` ` ` `left ` `=` `allOnes << (j ` `+` `1` `)` ` ` `# l's after position i. right = 00000011` ` ` `right ` `=` `((` `1` `<< i) ` `-` `1` `)` ` ` `# All ls, except for 0s between` ` ` `# i and j. mask 11100011` ` ` `mask ` `=` `left | right` ` ` `# Clear bits j through i then put min there` ` ` `n_cleared ` `=` `n & mask` ` ` ` ` `# Move m into correct position.` ` ` `m_shifted ` `=` `m << i` ` ` `return` `(n_cleared | m_shifted)` `# Driver Code` `n ` `=` `1024` `# in Binary N = 10000000000` `m ` `=` `19` `# in Binary M = 10011` `i ` `=` `2` `; j ` `=` `6` `print` `(updateBits(n, m, i, j))` `# This code is contributed by Anant Agarwal.` |

## C#

`// C# program for implementation of` `// updateBits()` `using` `System;` `class` `GFG {` ` ` ` ` `// Function to updateBits M` ` ` `// insert to N.` ` ` `static` `int` `updateBits(` `int` `n, ` `int` `m,` ` ` `int` `i, ` `int` `j)` ` ` `{` ` ` ` ` `/* Create a mask to clear bits i` ` ` `through j in n. EXAMPLE: i = 2,` ` ` `j = 4. Result should be 11100011.` ` ` `For simplicity, we'll use just 8` ` ` `bits for the example. */` ` ` ` ` `// will equal sequence of all ls` ` ` `int` `allOnes = ~0;` ` ` ` ` `// ls before position j, then 0s.` ` ` `// left = 11100000` ` ` `int` `left= allOnes << (j + 1);` ` ` ` ` `// l's after position i.` ` ` `// right = 00000011` ` ` `int` `right = ((1 << i) - 1);` ` ` ` ` `// All ls, except for 0s between i` ` ` `// and j. mask 11100011` ` ` `int` `mask = left | right;` ` ` ` ` `/* Clear bits j through i then put` ` ` `min there */` ` ` `// Clear bits j through i.` ` ` `int` `n_cleared = n & mask;` ` ` ` ` `// Move m into correct position.` ` ` `int` `m_shifted = m << i; ` ` ` ` ` `// OR them, and we're done!` ` ` `return` `(n_cleared | m_shifted);` ` ` `}` ` ` ` ` `public` `static` `void` `Main()` ` ` `{` ` ` ` ` `// in Binary N= 10000000000` ` ` `int` `n = 1024;` ` ` ` ` `// in Binary M= 10011` ` ` `int` `m = 19; ` ` ` `int` `i = 2, j = 6;` ` ` ` ` `Console.WriteLine(updateBits(n, m, i, j));` ` ` `}` `}` `//This code is contributed by Anant Agarwal.` |

## PHP

`<?php` `// PHP program for implementation` `// of updateBits()` `// Function to updateBits` `// M insert to N.` `function` `updateBits(` `$n` `, ` `$m` `, ` `$i` `, ` `$j` `)` `{` ` ` `// Create a mask to clear` ` ` `// bits i through j in n.` ` ` `// EXAMPLE: i = 2, j = 4.` ` ` `// Result should be 11100011.` ` ` `// For simplicity, we'll use` ` ` `// just 8 bits for the example.` ` ` `// will equal sequence of all ls` ` ` `$allOnes` `= ~0;` ` ` `// ls before position j, then` ` ` `// 0s. left = 11100000` ` ` `$left` `= ` `$allOnes` `<< (` `$j` `+ 1);` ` ` `// l's after position i.` ` ` `// right = 00000011` ` ` `$right` `= ((1 << ` `$i` `) - 1);` ` ` `// All ls, except for 0s between` ` ` `// i and j. mask 11100011` ` ` `$mask` `= ` `$left` `| ` `$right` `;` ` ` `// Clear bits j through i` ` ` `// then put min there` ` ` ` ` `// Clear bits j through i.` ` ` `$n_cleared` `= ` `$n` `& ` `$mask` `;` ` ` ` ` `// Move m into correct position.` ` ` `$m_shifted` `= ` `$m` `<< ` `$i` `;` ` ` `// OR them, and we're done!` ` ` `return` `(` `$n_cleared` `| ` `$m_shifted` `);` `}` `// Driver Code` `// in Binary N= 10000000000` `$n` `= 1024;` `// in Binary M= 10011` `$m` `= 19;` `$i` `= 2;` `$j` `= 6;` `echo` `updateBits(` `$n` `, ` `$m` `, ` `$i` `, ` `$j` `);` `// This code is contributed by Ajit` `?>` |

## Javascript

`<script>` `// JavaScript program for implementation of updateBits()` ` ` `// Function to updateBits M insert to N.` ` ` `function` `updateBits(n,m,i,j)` ` ` `{` ` ` `/* Create a mask to clear bits i through j` ` ` `in n. EXAMPLE: i = 2, j = 4. Result` ` ` `should be 11100011. For simplicity, we'll` ` ` `use just 8 bits for the example. */` ` ` ` ` `let allOnes = ~0; ` `// will equal sequence of all ls` ` ` ` ` `// ls before position j, then 0s. left = 11100000` ` ` `let left= allOnes << (j + 1);` ` ` ` ` `// l's after position i. right = 00000011` ` ` `let right = ((1 << i) - 1);` ` ` ` ` `// All ls, except for 0s between i and j. mask 11100011` ` ` `let mask = left | right;` ` ` ` ` `/* Clear bits j through i then put min there */` ` ` `// Clear bits j through i.` ` ` `let n_cleared = n & mask;` ` ` `// Move m into correct position.` ` ` `let m_shifted = m << i;` ` ` ` ` `// OR them, and we're done!` ` ` `return` `(n_cleared | m_shifted);` ` ` `}` ` ` ` ` ` ` `// in Binary N= 10000000000` ` ` `let n = 1024;` ` ` ` ` `// in Binary M= 10011` ` ` `let m = 19;` ` ` ` ` `let i = 2, j = 6;` ` ` ` ` `document.write(updateBits(n,m,i,j));` ` ` `// This code is contributed by sravan` `</script>` |

**Output:**

1100 // in Binary (10001001100)_{2}

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