# Count of carry operations on adding two Binary numbers

Given two decimal numbers **num1** and **num2**, the task is to count the number of times carry operation is required while adding the two given numbers in binary form.

**Examples:**

Input:num1 = 15, num2 = 10Output:3Explanation:

Give numbers are added as:

15 -> 1 1 1 1

10 -> 1 0 1 0

carry -> 1 1 1 – –

——————————

25 -> 1 1 0 0 1

Input:num1 = 14 num2 = 4Output:2Explanation:

Give numbers are added as:

14 -> 1 1 1 0

4 -> 0 1 0 0

carry -> 1 1 – – –

——————————

18 -> 1 0 0 1 0

**Naive Approach:** The naive idea is to convert the numbers into binary and add a bit one by one starting from Least Significant Bit and check if carry is generated or not. Whenever a carry is generated then increase the count by 1. Print count of **carry** after all the steps.

**Time Complexity:** O(K), where K is a count of the number of digits in the binary representation of X.**Auxiliary Space:** O(log N)

**Efficient Approach:** The idea is to use* *Bitwise XOR and AND. Below are the steps:

- Add the two binary numbers using XOR and AND.
- Now, the number of 1’s in the Bitwise AND of two numbers shows the number of
**carry**bits at that step. - Add the number of one’s in each stage in the above step to get the final count of
**carry**operation.

Below is the implementation of the above approach:

## C++

`// C++ Program for the above approach` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// Function to count the number of carry` `// operations to add two binary numbers` `int` `carryCount(` `int` `num1, ` `int` `num2)` `{` ` ` `// To Store the carry count` ` ` `int` `count = 0;` ` ` `// Iterate till there is no carry` ` ` `while` `(num2 != 0) {` ` ` `// Carry now contains common` ` ` `// set bits of x and y` ` ` `int` `carry = num1 & num2;` ` ` `// Sum of bits of x and y where at` ` ` `// least one of the bits is not set` ` ` `num1 = num1 ^ num2;` ` ` `// Carry is shifted by one` ` ` `// so that adding it to x` ` ` `// gives the required sum` ` ` `num2 = carry << 1;` ` ` `// Adding number of 1's of` ` ` `// carry to final count` ` ` `count += __builtin_popcount(num2);` ` ` `}` ` ` `// Return the final count` ` ` `return` `count;` `}` `// Driver Code` `int` `main()` `{` ` ` `// Given two numbers` ` ` `int` `A = 15, B = 10;` ` ` `// Function Call` ` ` `cout << carryCount(15, 10);` ` ` `return` `0;` `}` |

## Java

`// Java program for the above approach` `class` `GFG{` `// Function to count the number of carry` `// operations to add two binary numbers` `static` `int` `carryCount(` `int` `num1, ` `int` `num2)` `{` ` ` ` ` `// To Store the carry count` ` ` `int` `count = ` `0` `;` ` ` `// Iterate till there is no carry` ` ` `while` `(num2 != ` `0` `)` ` ` `{` ` ` ` ` `// Carry now contains common` ` ` `// set bits of x and y` ` ` `int` `carry = num1 & num2;` ` ` `// Sum of bits of x and y where at` ` ` `// least one of the bits is not set` ` ` `num1 = num1 ^ num2;` ` ` `// Carry is shifted by one` ` ` `// so that adding it to x` ` ` `// gives the required sum` ` ` `num2 = carry << ` `1` `;` ` ` `// Adding number of 1's of` ` ` `// carry to final count` ` ` `count += Integer.bitCount(num2);` ` ` `}` ` ` `// Return the final count` ` ` `return` `count;` `}` `// Driver Code` `public` `static` `void` `main(String[] args)` `{` ` ` ` ` `// Given two numbers` ` ` `int` `A = ` `15` `, B = ` `10` `;` ` ` `// Function call` ` ` `System.out.print(carryCount(A, B));` `}` `}` `// This code is contributed by Amit Katiyar` |

## Python3

`# Python3 program for the above approach` `# Function to count the number of carry` `# operations to add two binary numbers` `def` `carryCount(num1, num2):` ` ` `# To Store the carry count` ` ` `count ` `=` `0` ` ` `# Iterate till there is no carry` ` ` `while` `(num2 !` `=` `0` `):` ` ` `# Carry now contains common` ` ` `# set bits of x and y` ` ` `carry ` `=` `num1 & num2` ` ` `# Sum of bits of x and y where at` ` ` `# least one of the bits is not set` ` ` `num1 ` `=` `num1 ^ num2` ` ` `# Carry is shifted by one` ` ` `# so that adding it to x` ` ` `# gives the required sum` ` ` `num2 ` `=` `carry << ` `1` ` ` `# Adding number of 1's of` ` ` `# carry to final count` ` ` `count ` `+` `=` `bin` `(num2).count(` `'1'` `)` ` ` `# Return the final count` ` ` `return` `count` `# Driver Code` `# Given two numbers` `A ` `=` `15` `B ` `=` `10` `# Function call` `print` `(carryCount(A, B))` `# This code is contributed by Shivam Singh` |

## C#

`// C# program for the above approach` `using` `System;` `class` `GFG{` ` ` `static` `int` `countSetBits(` `int` `x)` `{` ` ` `int` `setBits = 0;` ` ` `while` `(x != 0)` ` ` `{` ` ` `x = x & (x - 1);` ` ` `setBits++;` ` ` `}` ` ` `return` `setBits;` `}` `// Function to count the number of carry` `// operations to add two binary numbers` `static` `int` `carryCount(` `int` `num1, ` `int` `num2)` `{` ` ` ` ` `// To Store the carry count` ` ` `int` `count = 0;` ` ` `// Iterate till there is no carry` ` ` `while` `(num2 != 0)` ` ` `{` ` ` ` ` `// Carry now contains common` ` ` `// set bits of x and y` ` ` `int` `carry = num1 & num2;` ` ` `// Sum of bits of x and y where at` ` ` `// least one of the bits is not set` ` ` `num1 = num1 ^ num2;` ` ` `// Carry is shifted by one` ` ` `// so that adding it to x` ` ` `// gives the required sum` ` ` `num2 = carry << 1;` ` ` `// Adding number of 1's of` ` ` `// carry to readonly count` ` ` `count += countSetBits(num2);` ` ` `}` ` ` `// Return the readonly count` ` ` `return` `count;` `}` `// Driver Code` `public` `static` `void` `Main(String[] args)` `{` ` ` ` ` `// Given two numbers` ` ` `int` `A = 15, B = 10;` ` ` `// Function call` ` ` `Console.Write(carryCount(A, B));` `}` `}` `// This code is contributed by Rohit_ranjan` |

## Javascript

`<script>` `// JavaScript program for the` `// above approach` ` ` `function` `countSetBits(x)` `{` ` ` `let setBits = 0;` ` ` `while` `(x != 0)` ` ` `{` ` ` `x = x & (x - 1);` ` ` `setBits++;` ` ` `}` ` ` `return` `setBits;` `}` `// Function to count the number of carry` `// operations to add two binary numbers` `function` `carryCount(num1, num2)` `{` ` ` ` ` `// To Store the carry count` ` ` `let count = 0;` ` ` ` ` `// Iterate till there is no carry` ` ` `while` `(num2 != 0)` ` ` `{` ` ` ` ` `// Carry now contains common` ` ` `// set bits of x and y` ` ` `let carry = num1 & num2;` ` ` ` ` `// Sum of bits of x and y where at` ` ` `// least one of the bits is not set` ` ` `num1 = num1 ^ num2;` ` ` ` ` `// Carry is shifted by one` ` ` `// so that adding it to x` ` ` `// gives the required sum` ` ` `num2 = carry << 1;` ` ` ` ` `// Adding number of 1's of` ` ` `// carry to readonly count` ` ` `count += countSetBits(num2);` ` ` `}` ` ` ` ` `// Return the readonly count` ` ` `return` `count;` `}` `// Driver Code` ` ` ` ` `// Given two numbers` ` ` `let A = 15, B = 10;` ` ` ` ` `// Function call` ` ` `document.write(carryCount(A, B));` `</script>` |

**Output:**

3

**Time Complexity:** O(log_{2}(N))**Auxiliary Space:** O(1)

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