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!