# NAND Gate

**NAND gate**.

**NAND gate**. The basis logical construction of the

**NAND gate**is shown below, The symbol of NAND gate is similar to AND gate but one bubble is drawn at the output point of the AND gate, in the case of NAND gate.

NAND gate actually means “not AND gate” which means, the output of this gate is just reverse of that of a similar AND gate.

We know that the output of the AND gate is only high or 1, when all the inputs are high or 1. In all other cases, the output of AND gate is low or 0. In the case NAND, the case is a just opposite, here, the output is only low or 0 when and only when all inputs of the gate are 1 and in all other cases, the output of NAND gate is high or 1.

Hence, truth table of a NAND gate can be written like,
Just reverse of the truth table of AND gate which is
Like AND gate a NAND gate can also be more than two inputs, like 3, 4, input NAND gate.

An NAND gate is also referred as universal logic gate as all the binary operations can be realized by using only NAND gates.

There are three basic binary operations, AND, OR and NOT. By these three basic operations, one can realize all complex binary operations. Now, we will show all these three binary operations can be realized by using only NAND gates.

## Realizing NOT Gate Using NAND Gate

When, both inputs of a two inputs NAND gate are zero, the output is 1 and both inputs of the NAND gate are 1, the output is 0. Hence a NOT gate can very easily be realized from NAND gate just by applying common inputs to the NAND gate. This is done by short circuiting all the inputs terminals of a NAND gate. Where, x is either 1 or 0.## Realizing AND Gate Using NAND Gate

As we told earlier, a NAND gate is a NOT gate followed by an AND gate, so if we can cancel the effect of NOT gate in a NAND gate it will become an AND gate. Hence, a NOT gate followed by a NAND gate realizes an AND gate. In this case we use the NOT gate which is realized from NAND gate and the logic circuit is shown below,## Realizing OR Gate from NAND Gate

From De Morgan Theorem we know, The above equation is a logical OR operation. The above logic equation can be represented by gates as shown above, where inputs first inverted then passed through a third NAND gate.The truth table of such circuit is, Now, we have proved that all three basic binary operations can be realized by using only NAND gates. Hence, any other simple or complex binary operation must also be realized by using only NAND gates and hence it is justified to call an

**NAND gates**as universal gates.

**Comments/Feedbacks**

Closely Related Articles OR Operation | Logical OR OperationAND Operation | Logical AND OperationLogical OR GateLogical AND GateNOT GateUniversal Gate | NAND and NOR Gate as Universal GateDiode and Transistor NAND Gate or DTL NAND Gate and NAND Gate ICsX OR Gate and X NOR GateTransistor Transistor Logic or TTLNOR GateFan out of Logic GatesINHIBIT GateNMOS Logic and PMOS LogicSchmitt GatesLogic Families Significance and Types of Logic FamiliesMore Related Articles Digital ElectronicsBoolean Algebra Theorems and Laws of Boolean AlgebraDe Morgan Theorem and Demorgans LawsTruth Tables for Digital LogicBinary Arithmetic Binary AdditionBinary SubtractionSimplifying Boolean Expression using K MapBinary DivisionExcess 3 Code Addition and SubtractionK Map or Karnaugh MapSwitching Algebra or Boolean AlgebraBinary MultiplicationParallel SubtractorBinary Adder Half and Full AdderBinary SubstractorSeven Segment DisplayBinary to Gray Code Converter and Grey to Binary Code ConverterBinary to BCD Code ConverterAnalog to Digital ConverterDigital Encoder or Binary EncoderBinary DecoderBasic Digital CounterDigital ComparatorBCD to Seven Segment DecoderParallel AdderParallel Adder or SubtractorMultiplexerDemultiplexer555 Timer and 555 Timer WorkingLook Ahead Carry AdderBinary Number System | Binary to Decimal and Decimal to Binary ConversionBinary to Decimal and Decimal to Binary ConversionBCD or Binary Coded Decimal | BCD Conversion Addition SubtractionBinary to Octal and Octal to Binary ConversionOctal to Decimal and Decimal to Octal ConversionBinary to Hexadecimal and Hex to Binary ConversionHexadecimal to Decimal and Decimal to Hexadecimal ConversionGray Code | Binary to Gray Code and that to Binary ConversionOctal Number SystemDigital Logic Gates2′s Complement1′s ComplementASCII CodeHamming Code2s Complement ArithmeticError Detection and Correction Codes9s complement and 10s complement | SubtractionSome Common Applications of Logic GatesKeyboard EncoderAlphanumeric codes | ASCII code | EBCDIC code | UNICODELatches and Flip FlopsS R Flip Flop S R LatchActive Low S R Latch and Flip FlopGated S R Latches or Clocked S R Flip FlopsD Flip Flop or D LatchJ K Flip FlopMaster Slave Flip FlopRead Only Memory | ROMProgrammable Logic DevicesProgrammable Array LogicApplication of Flip FlopsShift RegistersBuffer Register and Controlled Buffer RegisterData Transfer in Shift RegistersSerial In Serial Out (SISO) Shift RegisterSerial in Parallel Out (SIPO) Shift RegisterParallel in Serial Out (PISO) Shift RegisterParallel in Parallel Out (PIPO) Shift RegisterUniversal Shift RegistersBidirectional Shift RegisterDynamic Shift RegisterApplications of Shift RegistersUninterruptible Power Supply | UPSConversion of Flip FlopsJohnson CounterSequence GeneratorRing CounterNew Articles Principle of Water Content Test of Insulating OilCollecting Oil Sample from Oil Immersed Electrical EquipmentCauses of Insulating Oil DeteriorationAcidity Test of Transformer Insulating OilMagnetic Flux