 in boolean functions and propositional calculus, the sheffer stroke, named after henry m. sheffer, written "|" (see vertical bar, not to be confused with "||" which is often used to represent disjunction), "dpq", or "â" (an upwards arrow), denotes a logical operation that is equivalent to the negation of the conjunction operation, expressed in ordinary language as "not both". it is also called nand ("not and") or the alternative denial, since it says in effect that at least one of its operands is false. in boolean algebra and digital electronics it is known as the nand operation. like its dual, the nor operator (also known as the peirce arrow or quine dagger), nand can be used by itself, without any other logical operator, to constitute a logical formal system (making nand functionally complete). this property makes the nand gate crucial to modern digital electronics, including its use in nand flash memory and computer processor design. ==definition== the nand operation is a logical operation on two logical values. it produces a value of true, if â and only if â at least one of the propositions is false. ===truth table=== the truth table of a nand b (also written as a&nbsp;|&nbsp;b, dpq, or a&nbsp;â&nbsp;b) is as follows: {| class="wikitable" style="margin: 0 0 1em 1em" |- bgcolor="#ddeeff" align="center" |colspan=2|input || output |- bgcolor="#ddeeff" align="center" | a || b || a nand b |- bgcolor="#ddffdd" align="center" |0 || 0 || 1 |- bgcolor="#ddffdd" align="center" |0 || 1 || 1 |- bgcolor="#ddffdd" align="center" |1 || 0 || 1 |- bgcolor="#ddffdd" align="center" |1 || 1 || 0 |} ==history== the stroke is named after henry m. sheffer, who in 1913 published a paper in the transactions of the american mathematical society (sheffer 1913) providing an axiomatization of boolean algebras using the stroke, and proved its equivalence to a standard formulation thereof by huntington employing the familiar operators of propositional logic (and, or, not). because of self-duality of boolean algebras, sheffer's axioms are equally valid for either of the nand or nor operations in place of the stroke. sheffer interpreted the stroke as a sign for non-disjunction (n
Logic_gates Logic_symbols Logical_connectives