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We are given an integer number let’s say, x and the task are to count the smaller numbers less than x whose XOR with x will result in a value greater than the XOR value.

**The truth table for XOR operation is given below**

A | B | A XOR B |

0 | 0 | 0 |

1 | 0 | 1 |

0 | 1 | 1 |

1 | 1 | 0 |

**Input** − int x = 11

**Output** − Count of smaller values whose XOR with x is greater than x are − 4

**Explanation** −

We are given with the x as 11 which means we need to find XOR of x with the numbers less than x. So the numbers are 1 XOR 11 < 11(FALSE), 2 XOR 11 < 11(FALSE), 3 XOR 11 < 11(FALSE), 4 XOR 11 > 11(TRUE), 5 XOR 11 > 11(TRUE), 6 XOR 11 > 11(TRUE), 7 XOR 11> 11(TRUE), 8 XOR 11< 11(FALSE), 9 XOR 11 < 11(FALSE), 10 XOR 11 < 11(FALSE).

**Input**-: int x = 12

**Output** − Count of smaller values whose XOR with x is greater than x are − 11

**Explanation** −

We are given with the x as 12 which means we need to find XOR of x with the numbers less than x. So the numbers are 1 XOR 12 > 12(TRUE), 2 XOR 12 > 12(TRUE), 3 XOR 12 > 12(TRUE), 4 XOR 12 < 12(FALSE), 5 XOR 12 < 12(FALSE), 6 XOR 12 < 12(FALSE), 7 XOR 12< 12(FALSE), 8 XOR 12< 12(FALSE), 9 XOR 12 < 12(FALSE), 10 XOR 12 < 12(FALSE), 11 XOR 12 < 12(FALSE).

Input an integer element and store it in a variable named x.

Pass the value of num to the function for further processing

Create a temporary variable count to store the result and a variable named num and set it to 1.

Start loop WHILE till x != 0

Inside the loop, check IF x%2 == 0 then set the count as count + num

Set num as num * 2 and x as x / 2

Return the count

Print the result

#include using namespace std; int XOR_smaller(int x){ int count = 0; int num = 1; while (x != 0){ if (x%2 == 0){ count = count + num; } num = num*2; x = x/2; } return count; } int main(){ int x = 20; cout<<"Count of smaller values whose XOR with x is greater than x are: "<<XOR_smaller(x); return 0; }

If we run the above code it will generate the following output −

Count of smaller values whose XOR with x is greater than x are: 11

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