Just as all
boolean expressions can be implemented with just the
NAND function, the same is true for the NOR
function. We simply use various combinations of NOR to obtain other basic
boolean functions such as
AND,
OR, and
NOT, from which we can build more
complex functions. The following should help illustrate this concept. The NOR function is indicated (here at least) by the ↓ (downward arrow) character.
The NOR truth table
A B A↓B
-------------
T T F
T F F
F T F
F F T
Consider A↓A
A A↓A
---------
T F
F T
Thus, A↓A is equivalent to ¬A.
Now to find the ∨ (
or) function
A B A↓B (A↓B)↓(A↓B)
--------------------------
T T F T
T F F T
F T F T
F F T F
So we have (A↓B)↓(A↓B)
equivalent to A ∨ B (A or B)
From this point, we can achieve the
conjunction (
and) function as A∧B is equivalent to ¬(¬A∨¬B).
Therefore, A∧B (A and B) can be represented in NOR terms as
(((A↓A)↓B)↓((A↓A)↓B))↓(((A↓A)↓B)↓((A↓A)↓B))
Simple!