NAND


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NAND

[nand]
(mathematics)
A logic operator having the characteristic that if P, Q, R, … are statements, then the NAND of P, Q, R, … is true if at least one statement is false, false if all statements are true. Derived from NOT-AND. Also known as sheffer stroke.

NAND

Not AND.

The Boolean function which is true unless both its arguments are true, the logical complement of AND:

A NAND B = NOT (A AND B) = (NOT A) OR (NOT B)

Its truth table is:

A | B | A NAND B --+---+--------- F | F | T F | T | T T | F | T T | T | F

NAND, like NOR, forms a complete set of Boolean functions on its own since it can be used to make NOT, AND, OR and any other Boolean function:

NOT A = A NAND A

A AND B = NOT (A NAND B)

A OR B = (NOT A) NAND (NOT B)

NAND

(1) See NAND flash.

(2) (Not AND) A Boolean logic operation that is true if any single input is false. Two-input NAND gates are often used as the sole logic element on gate array chips, because all Boolean operations can be created from NAND gates. See flash memory.


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