C++ Boolean Algebra

Question

I have declared some variable as Boolean and I was hoping that C++ would know what to do when I did some boolean addition but it's not happening the way I would like it to. How do I get it to work.

#include<iostream>

using namespace std;

int main()
{
bool x,j;
x=0;
j=1;
for(int i=0;i<10;i++)
{
cout << x;
x=x+j;
}
return 0;
}

I am getting the output as

011111111

whereas I was hoping to get

0101010101

I was hoping that Boolean variables would mod out by 2. So if

x=1 then
x+1 = 0
x+1+1=1
x+1+1+1=0

and so on.

Am I confusing boolean algebra with base-2 algebra?

Thanks

Answer 1

bool x,j;
x=x+j;

This statement automatically promotes x and j to type int before adding them. Then the assignment converts back to bool in the usual way: 0 becomes false, but any other number , including 2, becomes true.

You can get Z_2 addition by using the ^ (xor) operator instead:

x = x^j;

Answer 2

C/C++ provide a range of bitwise operators: &, |, ^, ~, which generally work on booleans because true is converted to the integer 1 and false to 0.

But you can also use real boolean operators:

• && conjunction
• || disjunction
• != exclusive or (what you regard as addition)
• ! not