The logical operators that are used in bit string flicking are:
AND, OR, XOR, and NOT
Note that these Boolean, logical operators are often written in upper-case letters. Sometimes, we use the following symbols in place instead of these operators.
AND is represented as &
OR is represented as | (known as the vertical pipe)
XOR is represented as 
(in C++, it is represented as the caret, ^)
NOT is represented as ~ (known as a tilde)
You apply these logical operators on a "bit by bit" basis. Of course, the bit 1 is evaluated as TRUE and the bit 0 is evaluated as FALSE. The logical operators apply just like they do in Boolean logic. Remember that AND is similar to mathematical multiplication and that OR is like addition.
Some real easy examples:
1 & 1 = 1
1 | 0 = 1 0 | 0 = 0
1 & 0 = 0 1 0
= 1
More complicated examples:
101
& 110 = 100
1100 | 0100 = 1100 101
110
= 011
The color coding in the examples above depict the fact that the logical operators work on a bit by bit basis since the like colored bits are evaluated 2 at a time.
The NOT operator applies just like the negative sign in mathematics except, of course, the "negative" of 1 is 0 in Boolean logic and vice versa.
Examples:
~1 = 0 ~10111 = 01000 ~(111 & 100) = ~100 = 011
Note that in the case of bit strings, you may not disregard leading 0's as you would in mathematics or even binary arithmetic. That is, in binary arithmetic one can subtract the binary numbers
111
- 101
-----
010
and simplify that answer to simply 10
but in bit string flicking you must NEVER drop off a leading 0 bit because every bit has meaning usually. Since bit strings are often used as a set of flags or since the lead bit may indicate a number being negative or positive, you cannot disregard the leading 0 if there is one.
Another logical operator is the XOR. It is sometimes called the "eXclusive OR " operator. It works as the phrase "...either....or....but not both " is defined in the English language. For example,
a XOR b is true if either bit a is TRUE or bit b is TRUE but not both. So,
1 XOR 0 = 1 and 0 XOR 1 = 1 and 1 XOR
1 = 0 and 0
0 = 0
10110 XOR 00101 = 10011 (remember to evaluate the expression on a bit by bit basis)
Yet another logical operator is XNOR. It is sometimes called the eXclusive NOR. It is true if both of its arguments are the same (either 1 or 0). It is the opposite of XOR and is equivalent to ~(A XOR B).
For example, 1011 XNOR 1110 = 1010
You should memorize or be able to reproduce the following truth table that summarizes the AND, OR, XOR, and NOT logical operations.
|
A
|
B
|
A AND B
|
A OR B
|
A XOR B
|
A XNOR B
|
NOT A
|
|
0
|
0
|
0
|
0
|
0
|
1
|
1
|
|
0
|
1
|
0
|
1
|
1
|
0
|
1
|
|
1
|
0
|
0
|
1
|
1
|
0
|
0
|
|
1
|
1
|
1
|
1
|
0
|
1
|
0
|