Contents > Logic Gates

XOR

XOR is a two-input gate that outputs the exclusive disjunction of its inputs. That is, it outputs 1 only when the inputs are unequal.

From De Morgan's laws:

A ⊕ B

= (A ≠ B)

= AB + AB

= AA + AB + AB + BB

= A(A + B) + B(A + B)

= A C + B C, C = A + B

= A + C + B + C, C = A + B

That suggests the following construction of XOR from 3 NOR gates and an OR gate.

The code below is based on that schematic.

xor.t
ih -2
ih 2
iv -4
iv 3
_norLeft 0 1
lu -2
ju 1
notLeft 2 5
notRight -3 5
ih 0

in a -4..-1 0
in b 0..3 0
out o -2..1 11

_norLeft is a compact NOR gate composed of two O-tetrominoes. It is detailed in a later section.

Here are the results for all input combinations:

The L- and J-tetrominoes resting on the O-tetrominoes and the vertical I-tetrominoes act as wires. The bases of the inverters serve as OR gates, making them function as NORs. And the horizontal I-tetromino at the top operates as an OR gate.