binary bitwise operators
The binary bitwise operators are & , | , ^ , aka AND , OR , XOR.

AND, &
AND and & , the bitwise AND operators, AND the left and right operands on a bit by bit basis.

XOR, ^
XOR and ^ , the bitsize XOR operators, XOR the left and right operands on a bit by bit basis.

OR, |
OR and | , the bitwise OR operators, OR the left and right operands on a bit by bit basis.

binary logical operators
The binary logical operators are && , ^^ , ||.

&&
&&, the logical AND operator, returns XLONG $$TRUE if both the left and right operand is non-zero; otherwise it returns $$FALSE.

^^
^^ , the logical XOR operator, returns XLONG $$TRUE if either one but not both of the left and right operands is non-zero; otherwise it returns $$FALSE.

||
|| , the logical OR operator, returns XLONG $$TRUE if either one or both of the left and right operands is non-zero; otherwise it returns $$FALSE.

binary string operators
The only binary string operator is +.

+
+ , the string concatenate operator, appends the right string operand to the end of the left string operand. + also adds numeric and complex values; see Binary Arithmetic Operators.