How to make a bitwise NOR gate

Question

I\'m trying to understand the code from an answer I received earlier today:

a=0b01100001
b=0b01100010

bin((a ^ 0b11111111) & (b ^ 0b11111111))
         


        

Answer 1

a ^ 0b11111111      #exclusive or's each bit in a with 1, inverting each bit

>>> a=0b01100001
>>> bin(a ^ 0b11111111)
'0b10011110' 

>>> bin((a ^ 0b11111111) & (b ^ 0b11111111))
'0b10011100'

This is different than using the ~ operator since ~ returns a negative binary result.

>>> bin(~a & ~b)
'-0b1100100

The reason is the ~ operator inverts all bits used in representing the number, including the leading 0's that are not typically displayed, resulting in a 2's complement negative result. By using ^ and the 8 bit binary mask, only the first 8 bits are inverted.