NAND gate

NAND gate

Overview
Discussion

Encyclopedia
 INPUTA   B OUTPUT A NAND B 0 0 1 0 1 1 1 0 1 1 1 0

The Negated AND, NO AND or NAND gate is the opposite of the digital AND gate
AND gate
The AND gate is a basic digital logic gate that implements logical conjunction - it behaves according to the truth table to the right. A HIGH output results only if both the inputs to the AND gate are HIGH . If neither or only one input to the AND gate is HIGH, a LOW output results...

, and behaves in a manner that corresponds to the opposite of AND gate, as shown in the truth table on the right. A LOW output results only if both the inputs to the gate are HIGH. If one or both inputs are LOW, a HIGH output results.

The NAND gate is significant because any boolean function can be implemented by using a combination of NAND gates. This property is called functional completeness.

Digital systems employing certain logic circuits take advantage of NAND's functional completeness. In complicated logical expressions, normally written in terms of other logic functions such as AND
Logical conjunction
In logic and mathematics, a two-place logical operator and, also known as logical conjunction, results in true if both of its operands are true, otherwise the value of false....

, OR
Logical disjunction
In logic and mathematics, a two-place logical connective or, is a logical disjunction, also known as inclusive disjunction or alternation, that results in true whenever one or more of its operands are true. E.g. in this context, "A or B" is true if A is true, or if B is true, or if both A and B are...

, and NOT
Negation
In logic and mathematics, negation, also called logical complement, is an operation on propositions, truth values, or semantic values more generally. Intuitively, the negation of a proposition is true when that proposition is false, and vice versa. In classical logic negation is normally identified...

, writing these in terms of NAND saves on cost, because implementing such circuits using NAND gate yields a more compact result than the alternatives.

NAND gates can also be made with more than two inputs, yielding an output of LOW if all of the inputs are HIGH, and an output of HIGH if any of the inputs is LOW. These kinds of gates therefore operate as n-ary operators instead of a simple binary operator. Algebraically, these can be expressed as the function NAND(a, b, ..., n), which is logically equivalent
Logical equivalence
In logic, statements p and q are logically equivalent if they have the same logical content.Syntactically, p and q are equivalent if each can be proved from the other...

to NOT(a AND b AND ... AND n).

Symbols

There are three symbols for NAND gates: the 'distinctive' (MIL/ANSI
Ansi
Ansi is a village in Kaarma Parish, Saare County, on the island of Saaremaa, Estonia....

) symbol and the 'rectangular' IEC
International Electrotechnical Commission
The International Electrotechnical Commission is a non-profit, non-governmental international standards organization that prepares and publishes International Standards for all electrical, electronic and related technologies – collectively known as "electrotechnology"...

symbol, as well as a deprecated DIN
Din
DIN or Din or din can have several meanings:* A din is a loud noise.* Dīn, an Arabic term meaning "religion" or "way of life".* Din is one of the ten aspects of the Ein Sof in Kabbalah ....

symbol sometimes found on old schematics. For more information see logic gate symbols.
 MIL/ANSI Symbol' IEC Symbol DIN Symbol

Hardware description and pinout

NAND gates are basic logic gates, and as such they are recognised in TTL
Transistor-transistor logic
Transistor–transistor logic is a class of digital circuits built from bipolar junction transistors and resistors. It is called transistor–transistor logic because both the logic gating function and the amplifying function are performed by transistors .TTL is notable for being a widespread...

and CMOS
CMOS
Complementary metal–oxide–semiconductor is a technology for constructing integrated circuits. CMOS technology is used in microprocessors, microcontrollers, static RAM, and other digital logic circuits...

IC
Integrated circuit
An integrated circuit or monolithic integrated circuit is an electronic circuit manufactured by the patterned diffusion of trace elements into the surface of a thin substrate of semiconductor material...

s.

CMOS version

The standard, 4000 series
4000 series
The 4000 series is a family of industry standard integrated circuits which implement a variety of logic functions using Complementary Metal–Oxide–Semiconductor technology, and are still in use today. They were introduced by RCA as CD4000 COS/MOS series in 1968, as a lower power and more versatile...

, CMOS
CMOS
Complementary metal–oxide–semiconductor is a technology for constructing integrated circuits. CMOS technology is used in microprocessors, microcontrollers, static RAM, and other digital logic circuits...

IC
Integrated circuit
An integrated circuit or monolithic integrated circuit is an electronic circuit manufactured by the patterned diffusion of trace elements into the surface of a thin substrate of semiconductor material...

is the 4011, which includes four independent, two-input, NAND gates.

Availability

These devices are available from most semiconductor manufacturers such as Fairchild Semiconductor
Fairchild Semiconductor
Fairchild Semiconductor International, Inc. is an American semiconductor company based in San Jose, California. Founded in 1957, it was a pioneer in transistor and integrated circuit manufacturing...

, Philips
Philips
Koninklijke Philips Electronics N.V. , more commonly known as Philips, is a multinational Dutch electronics company....

or Texas Instruments
Texas Instruments
Texas Instruments Inc. , widely known as TI, is an American company based in Dallas, Texas, United States, which develops and commercializes semiconductor and computer technology...

. These are usually available in both through-hole DIL
Dual in-line package
In microelectronics, a dual in-line package is an electronic device package with a rectangular housing and two parallel rows of electrical connecting pins. The package may be through-hole mounted to a printed circuit board or inserted in a socket.A DIP is usually referred to as a DIPn, where n is...

and SOIC
Small-Outline Integrated Circuit
A small-outline integrated circuit is a surface-mounted integrated circuit package which occupies an area about 30–50% less than an equivalent DIP, with a typical thickness that is 70% less. They are generally available in the same pinouts as their counterpart DIP ICs...

format. Datasheets are readily available in most datasheet databases.

The standard 2-, 3-, 4- and 8-input NAND gates are available:
• CMOS
CMOS
Complementary metal–oxide–semiconductor is a technology for constructing integrated circuits. CMOS technology is used in microprocessors, microcontrollers, static RAM, and other digital logic circuits...

• 4011: Quad 2-input NAND gate
• 4023: Triple 3-input NAND gate
• 4012: Dual 4-input NAND gate
• 4068: Mono 8-input NAND gate
• TTL
Transistor-transistor logic
Transistor–transistor logic is a class of digital circuits built from bipolar junction transistors and resistors. It is called transistor–transistor logic because both the logic gating function and the amplifying function are performed by transistors .TTL is notable for being a widespread...

• 7400: Quad 2-input NAND gate
• 7410: Triple 3-input NAND gate
• 7420: Dual 4-input NAND gate
• 7430: Mono 8-input NAND gate

Implementations

The NAND gate has the property of functional completeness. That is, any other logic function (AND, OR, etc.) can be implemented
NAND logic
NAND gates are one of the two basic logic gates from which any other logic gates can be built. Due to this property, NAND and NOR gates are sometimes called "universal gates". However, modern integrated circuits are not constructed exclusively from a single type of gate...

using only NAND gates. An entire processor can be created using NAND gates alone. In TTL ICs using multiple-emitter transistors, it also requires fewer transistors than any other gate.

• AND gate
AND gate
The AND gate is a basic digital logic gate that implements logical conjunction - it behaves according to the truth table to the right. A HIGH output results only if both the inputs to the AND gate are HIGH . If neither or only one input to the AND gate is HIGH, a LOW output results...

• OR gate
OR gate
The OR gate is a digital logic gate that implements logical disjunction - it behaves according to the truth table to the right. A HIGH output results if one or both the inputs to the gate are HIGH . If neither input is HIGH, a LOW output results...

• NOT gate
• NOR gate
NOR gate
The NOR gate is a digital logic gate that implements logical NOR - it behaves according to the truth table to the right. A HIGH output results if both the inputs to the gate are LOW . If one or both input is HIGH , a LOW output results. NOR is the result of the negation of the OR operator...

• XOR gate
XOR gate
The XOR gate is a digital logic gate that implements an exclusive or; that is, a true output results if one, and only one, of the inputs to the gate is true . If both inputs are false or both are true , a false output results. Its behavior is summarized in the truth table shown on the right...

• Boolean algebra (logic)
• Logic gates
• NAND logic
NAND logic
NAND gates are one of the two basic logic gates from which any other logic gates can be built. Due to this property, NAND and NOR gates are sometimes called "universal gates". However, modern integrated circuits are not constructed exclusively from a single type of gate...

• Digital electronics