TexasInstruments 7400 chip, view and element placement

digital electronics Digital electronics is a field of electronics involving the study of digital signals and the engineering of devices that use or produce them. This is in contrast to analog electronics and analog signals. Digital electronic circuits are usual ...

, a NAND gate (NOT-AND) is a

logic gate A logic gate is an idealized or physical device implementing a Boolean function, a logical operation performed on one or more binary inputs that produces a single binary output. Depending on the context, the term may refer to an ideal logic gate, ...

which produces an output which is false only if all its inputs are true; thus its output is

complement A complement is something that completes something else. Complement may refer specifically to: The arts * Complement (music), an interval that, when added to another, spans an octave ** Aggregate complementation, the separation of pitch-clas ...

to that of an

AND gate The AND gate is a basic digital logic gate that implements logical conjunction (∧) from mathematical logic AND gate behaves according to the truth table. A HIGH output (1) results only if all the inputs to the AND gate are HIGH (1). If not all ...

. A LOW (0) output results only if all the inputs to the gate are HIGH (1); if any input is LOW (0), a HIGH (1) output results. A NAND gate is made using transistors and junction diodes. By

De Morgan's laws In propositional logic and Boolean algebra, De Morgan's laws, also known as De Morgan's theorem, are a pair of transformation rules that are both valid rules of inference. They are named after Augustus De Morgan, a 19th-century British mathem ...

, a two-input NAND gate's logic may be expressed as =+, making a NAND gate equivalent to

inverters A power inverter, inverter or invertor is a power electronic device or circuitry that changes direct current (DC) to alternating current (AC). The resulting AC frequency obtained depends on the particular device employed. Inverters do the opp ...

followed by an

OR gate The OR gate is a digital logic gate that implements logical disjunction. The OR gate returns true if either or both of its inputs are true; otherwise it returns false. The input and output states are normally represented by different voltage le ...

. The NAND gate is significant because any

boolean function In mathematics, a Boolean function is a function whose arguments and result assume values from a two-element set (usually , or ). Alternative names are switching function, used especially in older computer science literature, and truth function ( ...

can be implemented by using a combination of NAND gates. This property is called

functional completeness In logic, a functionally complete set of logical connectives or Boolean operators is one which can be used to express all possible truth tables by combining members of the set into a Boolean expression.. ("Complete set of logical connectives").. (" ...

. It shares this property with the

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 (1) results if both the inputs to the gate are LOW (0); if one or both input is HIGH (1), a LOW output (0 ...

. Digital systems employing certain logic circuits take advantage of NAND's functional completeness. The function is

logically equivalent Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premise ...

to One way of expressing A NAND B is

\overline

, where the symbol

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

. NAND gates with two or more inputs are available as

integrated circuit An integrated circuit or monolithic integrated circuit (also referred to as an IC, a chip, or a microchip) is a set of electronic circuits on one small flat piece (or "chip") of semiconductor material, usually silicon. Large numbers of tiny ...

s in transistor-transistor logic,

CMOS Complementary metal–oxide–semiconductor (CMOS, pronounced "sea-moss", ) is a type of metal–oxide–semiconductor field-effect transistor (MOSFET) fabrication process that uses complementary and symmetrical pairs of p-type and n-type MOSFE ...

, and other

logic families In computer engineering, a logic family is one of two related concepts: * A logic family of monolithic digital integrated circuit devices is a group of electronic logic gates constructed using one of several different designs, usually with compati ...

Symbols

There are three symbols for NAND gates: the MIL/

ANSI The American National Standards Institute (ANSI ) is a private non-profit organization that oversees the development of voluntary consensus standards for products, services, processes, systems, and personnel in the United States. The organi ...

symbol, the

IEC The International Electrotechnical Commission (IEC; in French: ''Commission électrotechnique internationale'') is an international standards organization that prepares and publishes international standards for all electrical, electronic and r ...

symbol and the deprecated DIN symbol sometimes found on old schematics. For more information see logic gate symbols. The ANSI symbol for the NAND gate is a standard AND gate with an inversion bubble connected.

Hardware description and pinout

NAND gates are basic logic gates, and as such they are recognised in

TTL TTL may refer to: Photography * Through-the-lens metering, a camera feature * Zenit TTL, an SLR film camera named for its TTL metering capability Technology * Time to live, a computer data lifespan-limiting mechanism * Transistor–transistor lo ...

and

ICs.

CMOS version

The standard, 4000 series,

IC 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 International, Inc. was an American semiconductor company based in San Jose, California. Founded in 1957 as a division of Fairchild Camera and Instrument, it became a pioneer in the manufacturing of transistors and of int ...

Philips Koninklijke Philips N.V. (), commonly shortened to Philips, is a Dutch multinational conglomerate corporation that was founded in Eindhoven in 1891. Since 1997, it has been mostly headquartered in Amsterdam, though the Benelux headquarters i ...

Texas Instruments Texas Instruments Incorporated (TI) is an American technology company headquartered in Dallas, Texas, that designs and manufactures semiconductors and various integrated circuits, which it sells to electronics designers and manufacturers globall ...

. These are usually available in both through-hole DIL and SOIC format. Datasheets are readily available in most datasheet databases. The standard 2-, 3-, 4- and 8-input NAND gates are available: *

** 4011: Quad 2-input NAND gate ** 4023: Triple 3-input NAND gate ** 4012: Dual 4-input NAND gate ** 4068: Mono 8-input NAND gate *

** 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

Functional completeness

The NAND gate has the property of

, which it shares with the

. That is, any other logic function (AND, OR, etc.) can be implemented using only NAND gates.Mano, M. Morris and Charles R. Kime. ''Logic and Computer Design Fundamentals, Third Edition.'' Prentice Hall, 2004. p. 73. An entire processor can be created using NAND gates alone. In TTL ICs using multiple-emitter

transistors upright=1.4, gate (G), body (B), source (S) and drain (D) terminals. The gate is separated from the body by an insulating layer (pink). A transistor is a semiconductor device used to Electronic amplifier, amplify or electronic switch, switch e ...

, it also requires fewer transistors than a NOR gate. As NOR gates are also functionally complete, if no specific NAND gates are available, one can be made from NOR gates using NOR logic.

References

External links

TTL NAND and AND gates
– All About Circuits {{Logical connectives

NAND gate In digital electronics, a NAND gate (NOT-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 an AND gate. A LOW (0) output results only if all the inputs to the ...