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. It deals with the relationship between Binary number, binary inputs and outputs by passing electrical s ...

, a NAND (NOT AND) gate is a

logic gate A logic gate is a device that performs 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, one that has, for ...

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 The AND gate is a basic digital logic gate that implements the logical conjunction (∧) from mathematical logic AND gates behave according to their truth table. A HIGH output (1) results only if all the inputs to the AND gate are HIGH (1). If a ...

. 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 calculus, 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 Validity (logic), valid rule of inference, rules of inference. They are nam ...

, a two-input NAND gate's logic may be expressed as

\overline \lor \overline = \overline

, making a NAND gate equivalent to inverters followed by an

OR gate The OR gate is a digital logic gate that implements logical disjunction. The OR gate outputs "true" if any of its inputs is "true"; otherwise it outputs "false". The input and output states are normally represented by different voltage levels. ...

. 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 functi ...

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

functional completeness In Mathematical logic, logic, a functionally complete set of logical connectives or Boolean function, Boolean operators is one that can be used to express all possible truth tables by combining members of the Set (mathematics), set into a Boolean ...

". It shares this property with the

NOR gate The NOR (NOT OR) 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 o ...

. Digital systems employing certain logic circuits take advantage of NAND's functional completeness. NAND gates with two or more inputs are available as

integrated circuit An integrated circuit (IC), also known as a microchip or simply chip, is a set of electronic circuits, consisting of various electronic components (such as transistors, resistors, and capacitors) and their interconnections. These components a ...

s in

transistor–transistor logic Transistor–transistor logic (TTL) is a logic family built from bipolar junction transistors (BJTs). Its name signifies that transistors perform both the logic function (the first "transistor") and the amplifying function (the second "transistor" ...

CMOS Complementary metal–oxide–semiconductor (CMOS, pronounced "sea-moss ", , ) is a type of MOSFET, metal–oxide–semiconductor field-effect transistor (MOSFET) semiconductor device fabrication, fabrication process that uses complementary an ...

, and other logic families.

Symbols

There are three symbols for NAND gates: the ''MIL/

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

'' symbol, the '' IEC'' symbol and the deprecated '' DIN'' symbol sometimes found on old schematics. The ANSI symbol for the NAND gate is a standard AND gate with an inversion bubble connected.

Logic

The function is logically equivalent 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

Implementations

The basic implementations can be understood from the image on the left below: If either of the switches S1 or S2 is open, the

pull-up resistor In electronic logic circuits, a pull-up resistor (PU) or pull-down resistor (PD) is a resistor used to ensure a known state for a signal. More specifically, a pull-up resistor or pull-down resistor ensures that a wire will have a high logic lev ...

R will set the output signal Q to 1 (high). If S1 and S2 are both closed, the pull-up resistor will be overridden by the switches, and the output will be 0 (low). In the

depletion-load NMOS logic In integrated circuits, depletion-load NMOS is a form of digital logic family that uses only a single power supply voltage, unlike earlier NMOS logic, NMOS (n-type metal-oxide semiconductor) logic families that needed multiple power supply voltag ...

realization in the middle below, the switches are the transistors T2 and T3, and the transistor T1 fulfills the function of the pull-up resistor. In the

realization on the right below, the switches are the n-type transistors T3 and T4, and the pull-up resistor is made up of the p-type transistors T1 and T2, which form the complement of transistors T3 and T4. Funktionsprinzip eines NAND-Gatters.svg, Implementation using switches and a pull-up resistor Nmos enhancement saturated nand.svg, NMOS Cmos nand.svg,

In CMOS, NAND gates are more efficient than NOR gates. This is due to the faster charge mobility in n-MOSFETs compared to p-MOSFETs, so that the parallel connection of two p-MOSFETs (T1 and T2) realised in the NAND gate is more favourable than their series connection in the NOR gate. For this reason, NAND gates are generally preferred over NOR gates in CMOS circuits.

Hardware design and pinout

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

ICs. The standard, 4000 series,

IC is the 4011, which includes four independent, two-input, NAND gates. These devices are available from many semiconductor manufacturers. These are usually available in both through-hole DIL and SOIC formats. Datasheets are readily available in most datasheet databases. The standard two-, three-, four- and eight-input NAND gates are available: *

** 4011: Quad two-input NAND gate ** 4023: Triple three-input NAND gate ** 4012: Dual four-input NAND gate ** 4068: Mono eight-input NAND gate * TTL ** 7400: Quad two-input NAND gate ** 7410: Triple three-input NAND gate ** 7420: Dual four-input NAND gate ** 7430: Mono eight-input NAND gate

Functional completeness

Construction of a NAND gate from NOR gates 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 A transistor is a semiconductor device used to Electronic amplifier, amplify or electronic switch, switch electrical signals and electric power, power. It is one of the basic building blocks of modern electronics. It is composed of semicondu ...

, 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
at All About Circuits {{Logical connectives

NAND gate In digital electronics, a NAND (NOT AND) gate 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 ...