A logical bitwise operator. NOR is a binary operator meaning it takes two inputs. The symbol for a NOR gate is the same as an OR gate with a dot a the front for negation.

The gate looks like this
   \-\
A---\ \
    | |0----Result
B---/ /
   /-/
The truth table is below.

A B Result
1 1 0
1 0 0
0 1 0
0 0 1
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!

Nor (?), conj. [OE. nor, contr. from nother. See Neither.]

A negative connective or particle, introducing the second member or clause of a negative proposition, following neither, or not, in the first member or clause (as or in affirmative propositions follows either). Nor is also used sometimes in the first member for neither, and sometimes the neither is omitted and implied by the use of nor.

Provide neither gold nor silver, nor brass, in your purses, nor scrip for your journey. Matt. x. 9, 10.

Where neither moth nor rust doth corrupt. Matt. vi. 20.

I love him not, nor fear him. Shak.

Where neither party is nor true, nor kind. Shak.

Simois nor Xanthus shall be wanting there. Dryden.

 

© Webster 1913.

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