Boolean algebra is a branch of mathematics that has become important due to its use in computing. In Boolean algebra values are expressed not as numbers but as being either TRUE or FALSE.
In mathematics, an operation acts on inputs to produce an output. For example, 3+1=4 takes the two inputs 3 and 1 and applies the addition operation to produce the output 4. In Boolean algebra, the NOR operation produces an output that is the negation of the logical OR of the inputs. That is, if two inputs are A and B, either of which may be TRUE or FALSE, then the output of A NOR B is given according to this truth table.
Thus, the logical NOR operation output is only TRUE when neither A nor B are TRUE.
The TRUE and FALSE states could represent actual physical states. For example, on printed pages, the input may be considered TRUE if there is ink on a page and FALSE if not. Then the NOR output would be TRUE if all pages are white and FALSE if any of the pages had ink on it.
Logical NOR may have any number of inputs. But regardless of the number of inputs, all inputs must be FALSE for the output to be TRUE.
As a historical trivia, the guidance computers for the Apollo missions were said to have been constructed (almost) entirely of three-input NORs.
For brevity, the NOR operation is often written in symbol form. One way of expressing NOR is
where the BAR above the symbols representing A OR B (denoted by the "v" symbol) indicates the negation of the OR operation.
Enough geek-speak ... on to the cache.
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