ONLINE ELECTRICAL ENGINEERING STUDY SITE

Truth Tables for Digital Logic

Truth tables list-out the output of a particular digital logic circuit for all the possible combinations of its inputs. This means that these truth tables can be used to deduce the logical expression for the given digital circuit.

NOT Gate or an Inverter

not gate or an inverter NOT gate is a single-in single-out logical device where the output will always be the complementary form of the input. This means that the output is 0 for input equal to 1 and vice versa, as indicated by the truth table. This is symbolically written as Y = X̅.

AND Gate

and gate truth table AND gate is a basic gate with multiple inputs and a single output. This gate has its output high only if all its inputs are one, failing which the output will be zero as shown by the truth table. The logical expression corresponding to this gate is given as Y = I1.I2.

OR Gate

OR is a type of basic gate with multi-input, single-output characteristic. Here the output is zero only if all of its input bits are zero as indicated by the truth table of 2-input OR gate. The logical expression for the OR gate is given as or gate truth table

NAND Gate

nand gate truth table NAND gate is logically equivalent to AND gate followed by a NOT gate. The truth table for this gate shows that the output of NAND gate is low only if all of its inputs are high (else it is one). This implies that the output of the NAND gate is the negated output of the AND gate, represented by the intermediate result M in the above truth table. Logical expression for the NAND gate is given by

NOR Gate

nor gate truth table NOR gate is a result of combining NOT gate with an OR gate. Thus its output is the negation of OR gate output which implies that it has high output only if all of its inputs are low. However for any other combination of inputs, the output will be low as shown by the truth table. Logical expression for the same can be given as

XOR Gate

xor gate truth table XOR gate is a logical device which has its output high only when its inputs are different, as shown by the truth table. This means that non-identical inputs result in high output of the gate while identical input bits cause the gate output to go low.

Logically this is given by Further in its expanded form, one gets In general XOR gate is used as a parity checker and can have multiple inputs.

XNOR gate

xnor gate truth table XNOR gate is a result of combining XOR gate with a NOT gate, which means that the output will be the inverted form of the XOR outputs. Thus one gets high output for identical inputs and low output for non-identical inputs, as shown by the truth table. Logical expression for the XNOR gate is given by This gate can also have multiple inputs and serves as a parity checker.

Closely Related Articles Digital ElectronicsBoolean Algebra Theorems and Laws of Boolean AlgebraDe Morgan Theorem and Demorgans LawsBinary Arithmetic Binary AdditionBinary SubtractionSimplifying Boolean Expression using K MapBinary DivisionExcess 3 Code Addition and SubtractionK Map or Karnaugh MapSwitching Algebra or Boolean AlgebraBinary MultiplicationParallel SubtractorMore Related Articles Binary 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 AdderOR Operation | Logical OR OperationAND Operation | Logical AND OperationLogical OR GateLogical AND GateNOT GateUniversal Gate | NAND and NOR Gate as Universal GateNAND 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 FamiliesBinary 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 FlopsNew Articles Resistance Variation with TemperatureLook Ahead Carry AdderGround Clearance of Different Transmission LinesWater Meter