Logical nor
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- This article is about logical nor. For the legendary eponymous king of Norway see Nór.
NOR.jpg
Logical nor (not or) or Webb-operation is a boolean logic operator which produces a result that is the inverse of logical or. That is, p nor q is only true when neither p nor q is true, and is false otherwise. A common means of writing p NOR q is <math>\overline{p + q}<math>, where the symbol <math>+<math> signifies OR and the line over the expression signifies not, the logical negation of that expression
The two-input logical NOR operator is commonly described by a truth table, describing the output state for all possible input combinations:
| A | B | A nor B |
|---|---|---|
| F | F | T |
| F | T | F |
| T | F | F |
| T | T | F |
NOR has the interesting feature that all other logical operators can be expressed by various functions of nor.
| "not p" is equivalent to "p NOR p" | <math>\overline{p} \equiv \overline{p + p}<math> |
| "p and q" is equivalent to "(p NOR p) NOR (q NOR q)" | <math>p \cdot q \equiv \overline{\overline{(p + p)} + \overline{(q + q)}}<math> |
| "p or q" is equivalent to "(p NOR q) NOR (p NOR q)" | <math>p + q \equiv \overline{\overline{(p + q)} + \overline{(p + q)}}<math> |
| "p implies q" is equivalent to "((p NOR q) NOR q) NOR ((p NOR q) NOR q)" | <math>p \rightarrow q \equiv \overline{\overline{(\overline{(p+q)} + q)}+\overline{(\overline{(p + q)} + q)}}<math> |
The logical nand operator also has this ability to express all logical operations.
The computer used in the spacecraft that first carried humans to the moon, the Apollo Guidance Computer, was constructed entirely using three input NOR gates.