Question

Write a program that reads an integer value from the keyboard into a variable of type int, and uses one of the bitwise operators (i.e. not the % operator!) to determine the positive remainder when divided by 8.

For example, 29 = (3×8)+5 and 14 = ( 2×8)+2 have positive remainder 5 and 2, respectively, when divided by 8.

I tried to search how can I solve it. What I did is to break given examples numbers into binary.

29 => 101001
8  => 001000
5 =>  000101

I don’t know what is operation I should do with 29 and 8 to get result 5 in binary.

While searching there’s some guys said that we should do (& operation with 7 )

remainder = remainder & 7 ;

Then I tried to do this with Value itself

value = value & 7 ; 

and Here’s my code After doing it …

#include <iostream>

using std::cout;
using std::endl;
using std::cin;

int main()
{
  int value = 0;
  int divisor = 8;
  int remainder = 0;

  cout << "Enter an integr and I'll divide it by 8 and give you the remainder!"
       <<endl;
  cin >> value;

  value = value & 7;
  remainder = value & divisor;
  cout << remainder;

  return 0;
}

It gave me result 0 when I use value 29. I don’t know what I wrote was right or not.

Answer 1

Since 8 is exactly 2^3, the modulo-8 remainder of any number is composed of its last three binary digits, i. e. it equals the number bitwise-and 7:

unsigned rem8 = number & 7;

(7 is 111 in binary, that’s why.)