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Sheffer interpreted the stroke as a sign for nondisjunction in his paper, mentioning non-conjunction only in a footnote and without a special sign for it. It was Jean Nicod who first used the stroke as a sign for non-conjunction (NAND) in a paper of 1917 and which has since become current practice.
For example, an axiom with six NAND operations and three variables is equivalent to Boolean algebra: [1] (()) ((())) = where the vertical bar represents the NAND logical operation (also known as the Sheffer stroke).
Sheffer stroke, the sign for the NAND operator (negation of conjunction). ... A new symbol made specifically for the NAND operator.
Because Sheffer's stroke (also known as NAND operator) is functionally complete, it can be used to create an entire formulation of propositional calculus. NAND formulations use a rule of inference called Nicod's modus ponens: , (). Nicod's axiom system: [5]
A "Boolean algebra" may be defined from any of several different bases. Three bases for Boolean algebra are in common use, the lattice basis, the ring basis, and the Sheffer stroke or NAND basis. These bases impart respectively a logical, an arithmetical, and a parsimonious character to the subject.
NAND or Sheffer stroke - true when it is not the case that all inputs are true ("not both") NOR or logical nor - true when none of the inputs are true ("neither") XNOR or logical equality - true when both inputs are the same ("equal") An example of a more complicated function is the majority function (of an odd number of inputs).
A CMOS transistor NAND element. V dd denotes positive voltage.. In CMOS logic, if both of the A and B inputs are high, then both the NMOS transistors (bottom half of the diagram) will conduct, neither of the PMOS transistors (top half) will conduct, and a conductive path will be established between the output and Vss (ground), bringing the output low.
The first published proof was by Henry M. Sheffer in 1913, so the NAND logical operation is sometimes called Sheffer stroke; the logical NOR is sometimes called Peirce's arrow. [23] Consequently, these gates are sometimes called universal logic gates. [24]