You seems be confused with the symbols of the operators. Theses symbols are actually split in two different categories, which are bit-wise operators and logical operators. Although they use the same symbols, you should regard them as different operators. The truth tables for both categories are similar, but the meanings are different. Maybe that's why people use the similar symbols for the operators.
bit-wise operators
~ // NOT
& // AND
| // OR
^ // XOR
The bit-wise operators will regard all its operands as binary numerals and act according to the bit-wise truth tables on every bit of the operands.
Bit-wise Truth Table
x y x&y x|y x^y
0 0 0 0 0
1 0 0 1 1
0 1 0 1 1
1 1 1 1 0
x ~x
0 1
1 0
logical operators
! // Logical NOT (negation)
&& // Logical AND (conjunction)
|| // Logical OR (disjunction)
The logical operator will regard all its operands as bools and act according the operator truth tables. Any number that is not equal to 0
will be true
, else will be false
.
Logical Truth Table
x y x&&y x||y
F F F F
T F F T
F T F T
T T T T
x !x
F T
T F
For example:
int a = 10; // a = 0000 .... 0000 1010 <-- a 32 bits integer
// a is not zero -> true
int b = 7; // b = 0000 .... 0000 0111 <-- a 32 bits integer
// b is not zero -> true
Then for bit-wise operator:
assert(a & b == 2); // 2 = 0000 .... 0000 0010 <-- every bit will & separately
For logic operator:
assert(a && b == true); // true && true -> true