The NAND, NOR, and XOR operators in Python

The NAND, NOR, and XOR operators are logical operators that are not built into Python, but can be implemented using the built-in not, and, and or operators. The NAND operator returns True if and only if both of its operands are False, and the NOR operator returns True if and only if both of its operands are False. The XOR operator returns True if and only if exactly one of its operands is True.

The NAND logic operator

As can be seen in the truth table below, the NAND operator returns True if and only of its operands are False this is the opposite of the and operator. That is because the not operator is applied to the result of the and operator which inverts the result.

A	B	Result
True	True	False
True	False	True
False	True	True
False	False	True

The NAND operator can be implemented in Python as follows:

The NAND logic in a Python function

def nand(a, b):
    return not (a and b)

If the nand function is called with True and False as its arguments, it will return True because the and operator returns False and the not operator inverts the result. This can also be directly implemented in a Python program as follows:

Using the NAND logic in a Python program

def main():
    a = True
    b = False
    if not (a and b):
        print("The NAND of", a, "and", b, "is True")
    else:
        print("The NAND of", a, "and", b, "is False")


if __name__ == "__main__":
    main()

The NOR logic operator

Like the NAND operator, the NOR operator returns True if and only if both of its operands are False. This is the opposite of the or operator. That is because the not operator is applied to the result of the or operator which inverts the result.

A	B	Result
True	True	False
True	False	False
False	True	False
False	False	True

The NOR operator can be implemented in Python as follows:

The NOR logic in a Python function

def nor(a, b):
    return not (a or b)

If the nor function is called with True and False as its arguments, it will return False because the or operator returns True and the not operator inverts the result. This can also be directly implemented in a Python program as follows:

Using the NOR logic in a Python program

def main():
    a = True
    b = False
    if not (a or b):
        print("The NOR of", a, "and", b, "is True")
    else:
        print("The NOR of", a, "and", b, "is False")


if __name__ == "__main__":
    main()

The XOR logic operator

Unlike the and and or operators, the XOR operator returns True if and only if exactly one of its operands is True. The truth table for the XOR operator is as follows and it can be implemented using the and, or, and not operators.

A	B	Result
True	True	False
True	False	True
False	True	True
False	False	False

The XOR operator can be implemented in Python as follows:

The XOR logic in a Python function

def xor(a, b):
    return (a and not b) or (not a and b)

If the xor function is called with True and False as its arguments, it will return True because the first part of the expression (a and not b) returns True and the second part of the expression (not a and b) returns True. This can also be directly implemented in a Python program as follows:

Using the XOR logic in a Python program

def main():
    a = True
    b = False
    if (a and not b) or (not a and b):
        print("The XOR of", a, "and", b, "is True")
    else:
        print("The XOR of", a, "and", b, "is False")


if __name__ == "__main__":
    main()

Note

The xor function can also be implemented using the ^ operator as follows:

The XOR logic in a Python function using the ^ operator

def xor(a, b):
    return a ^ b

The ^ operator returns True if and only if exactly one of its operands is True.

Note

The operator module in Python provides a function called xor that can be used to implement the XOR logic as follows:

The XOR logic in a Python function using the operator module

import operator

def xor(a, b):
    return operator.xor(a, b)

The XNOR logic operator

The XNOR operator returns True if and only if both of its operands are True or both of its operands are False. This is the opposite of the XOR operator. The truth table for the XNOR operator is as follows and it can be implemented using the and, or, and not operators.

A	B	Result
True	True	True
True	False	False
False	True	False
False	False	True

The xnor operator can be implemented in Python as follows:

The XNOR logic in a Python function

def xnor(a, b):
    return (a and b) or (not a and not b)

If the xnor function is called with True and False as its arguments, it will return False because the first part of the expression (a and b) returns False and the second part of the expression (not a and not b) returns True. This can also be directly implemented in a Python program as follows:

Using the XNOR logic in a Python program

def main():
    a = True
    b = False
    if (a and b) or (not a and not b):
        print("The XNOR of", a, "and", b, "is True")
    else:
        print("The XNOR of", a, "and", b, "is False")


if __name__ == "__main__":
    main()

Considerations about logical operators

The logical operators in Python are used to perform logical operations on boolean values. The and operator returns True if and only if both of its operands are True, the or operator returns True if and only if at least one of its operands is True, and the not operator returns True if and only if its operand is False. The and, or, and not operators can be combined to implement the NAND, NOR, XOR, and XNOR operators.

Other built-in operators like the ^ operator can also be used to implement the XOR operator, and the == operator can be used to implement the XNOR operator. The operator module in Python provides a function called xor that can be used to implement the XOR operator. The logical operators in Python are used to perform logical operations on boolean values, and can be combined to implement the NAND, NOR, XOR, and XNOR operators.

Convert numbers between numerical systems   Using magic method __contains__