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The Info List - NAND Gate


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In digital electronics, a N AND gate
AND gate
(negative-AND) is a logic gate which produces an output which is false only if all its inputs are true; thus its output is complement to that of the AND gate. A LOW (0) output results only if both the inputs to the gate are HIGH (1); if one or both inputs are LOW (0), a HIGH (1) output results. It is made using transistors and junction diodes. By De Morgan's theorem, AB=A+B, and thus a N AND gate
AND gate
is equivalent to inverters followed by an OR gate. The N AND gate
AND gate
is significant because any boolean function can be implemented by using a combination of NAND gates. This property is called functional completeness. It shares this property with the NOR gate. Digital systems employing certain logic circuits take advantage of NAND's functional completeness. The function NAND(a1, a2, ..., an) is logically equivalent to NOT(a1 AND a2 AND ... AND an). One way of expressing A NAND B is

A ∧ B

¯

displaystyle overline Aland B

, where the symbol

displaystyle land

signifies AND and the bar signifies the negation of the expression under it: in essence, simply

¬ ( A ∧ B )

displaystyle displaystyle neg (Aland B)

.

Contents

1 Symbols 2 Hardware description and pinout 3 Implementations

3.1 Alternatives

4 See also 5 References 6 External links

Symbols[edit] There are three symbols for NAND gates: the MIL/ ANSI
ANSI
symbol, the IEC symbol and the deprecated DIN
DIN
symbol sometimes found on old schematics. For more information see logic gate symbols. The ANSI symbol for the N AND gate
AND gate
is a standard AND gate
AND gate
with an inversion bubble connected.

MIL/ ANSI
ANSI
Symbol IEC Symbol DIN
DIN
Symbol

Hardware description and pinout[edit] NAND gates are basic logic gates, and as such they are recognised in TTL and CMOS
CMOS
ICs.

This schematic diagram shows the arrangement of NAND gates within a standard 4011 CMOS
CMOS
integrated circuit.

Implementations[edit] The N AND gate
AND gate
has the property of functional completeness. That is, any other logic function (AND, OR, etc.) can be implemented using only NAND gates.[1] An entire processor can be created using NAND gates alone. In TTL ICs using multiple-emitter transistors, it also requires fewer transistors than a NOR gate.

NMOS NAND gate

PMOS NAND gate

CMOS
CMOS
NAND gate

TTL NAND gate

The physical layout of a CMOS
CMOS
NAND

Die of a 74AHC00D quad 2-input N AND gate
AND gate
manufactured by NXP Semiconductors

Silicon implementation of 4 NAND gates in an integrated circuit

Alternatives[edit] Further information: NAND logic
NAND logic
and NOR logic If no specific NAND gates are available, one can be made from NOR gates, because NAND and NOR gates are considered the "universal gates", meaning that they can be used to make all the other gates.[1]

Desired gate NOR Construction

See also[edit]

AND gate OR gate NOT gate NOR gate XOR gate XNOR gate Boolean algebra Logic gate NAND logic Digital electronics

References[edit]

^ a b Mano, M. Morris and Charles R. Kime. Logic and Computer Design Fundamentals, Third Edition. Prentice Hall, 2004. p. 73.

External links[edit]

TTL NAND and AND gates - All About Circuits

Wikimedia Commons has media related to NAND gates.

v t e

Logical connectives

Tautology/True 

displaystyle top

Alternative denial (NAND gate) 

displaystyle uparrow

Converse implication 

displaystyle leftarrow

Implication (IMPLY gate) 

displaystyle rightarrow

Disjunction (OR gate) 

displaystyle lor

Negation (NOT gate) 

¬

displaystyle neg

Exclusive or (XOR gate) 

displaystyle nleftrightarrow

Biconditional (XNOR gate) 

displaystyle leftrightarrow

Statement

Joint denial (NOR gate) 

displaystyle downarrow

Nonimplication 

displaystyle nrightarrow

Converse nonimplication 

displaystyle nleftarrow

Conjunction (AND gate) 

displaystyle land

Contradiction/False 

.