# 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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In conjunction with Robert Forchheimer, Professor of Information Coding at LiU, Tybrandt has now taken the next step by developing chemical chips that also contain logic gates, such as NAND gates that allow for the construction of all logical functions.

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