Combinational circuits r011

Digital Electronics

1. Combinational Circuits
Combinationalcircuitisacircuitinwhichwe
combinethedifferentgatesinthecircuit.
forexampleadder,subtractor,encoder,decoder,
multiplexeranddemultiplexer.
Someofthecharacteristicsofcombinational
circuitsarefollowing:
•Theoutputofcombinationalcircuitatanyinstant
oftimedependsonlyonthelevelspresentatinput
terminals.
•Thecombinationalcircuitdonotuseanymemory.

2. •The previous state of input does not have any
effecton the present state of the circuit.
•A combinational circuit can have an n number
of inputs and m numberof outputs.
•Block diagram

3. Half Adder
•Halfadderisacombinationallogiccircuitwith
twoinputsandtwooutputs.
•Thehalfaddercircuitisdesignedtoaddtwo
singlebitbinarynumberAandB.
•Itisthebasicbuildingblockforadditionoftwo
singlebitnumbers.
•Thiscircuithastwooutputscarryandsum.

4. •Block diagram •Circuit Diagram
Truth Table

5. Full Adder
•Full adder is developed to overcome the
drawback of Half Adder circuit.
•It can add two one-bit numbers A and B, and
the output of two bit with input cin.
•The full adder is a three input and two output
combinational circuit.
•Block diagram

6. Circuit Diagram
Truth Table

7. Parallel Adder
•TheFullAdderiscapableofaddingonlytwo
singledigitbinarynumberalongwithacarry
input.
•Butinpracticalweneedtoaddbinary
numberswhicharemuchlongerthanjustone
bit.
•To add two n-bit binary numbers we need to
use the n-bit parallel adder.
•It uses a number of full adders in cascade.
•Thecarryoutputofthepreviousfulladderis
connectedtocarryinputofthenextfulladder.

8. 4-Bit Parallel Adder
•Intheblockdiagram,A
0andB
0representtheLSB
ofthefourbitwordsAandB.
•HenceFullAdder-0istheloweststage.Henceits
C
inhasbeenpermanentlymade0.
•Therestoftheconnectionsareexactlysameas
thoseofn-bitparalleladderisshowninfig.The
fourbitparalleladderisaverycommonlogic
circuit.

9. •Half Subtractor
•Halfsubtractorisacombinationcircuitwith
twoinputsandtwooutputs(differenceand
borrow).
•Itproducesthedifferencebetweenthetwo
binarybitsattheinputasadifference(i.eA-B).
•Italsoproducesanoutput(Borrow)to
indicateifa1hasbeenborrowed.
•Inthesubtraction(A-B),Aiscalledas
MinuendbitandBiscalledasSubtrahendbit.

10. •Block Diagram •Circuit Diagram
Truth Table

11. Full Subtractor
•Thedisadvantageofahalfsubtractoris
overcomebyfullsubtractor.
•Thefullsubtractorisacombinationalcircuit
withthreeinputsA,B,Candtwooutput
DifferenceandBorrow.
•TheinputareAisthe'minuend',Bis
'subtrahend',Cisthe'borrow'andproduced
bythepreviousstage.
•DisthedifferenceoutputandBistheborrow
output.

12. •Block diagram •Circuit Diagram
Truth Table

13. Parallel Subtractor
Thesubtractioncanbecarriedoutbytakingthe
1'sor2'scomplementofthenumbertobe
subtracted.
Forexamplewecanperformthesubtraction(A-
B)byaddingeither1'sor2'scomplementofB
toA.
Thatmeanswecanuseabinaryadderto
performthebinarysubtraction.

14. 4 Bit Parallel Subtractor
•Thenumbertobesubtracted(B)isfirstpassed
throughinverterstoobtainits1's
complement.
•The4-bitadderthenaddsAand2's
complementofBtoproducethesubtraction.
S
3S
2S
1S
0representstheresultofbinary
subtraction(A-B)andcarryoutputC
out
representsthepolarityoftheresult.
•IfA>BthenCout=0andtheresultofbinary
form(A-B)thenC
out=1andtheresultisinthe
2'scomplementform.

16. Multiplexers
•Multiplexerisaspecialtypeofcombinational
circuit.Therearen-datainputs,oneoutput
andmselectinputswith2m=n.Itisadigital
circuitwhichselectsoneofthendatainputs
androutesittotheoutput.Theselectionof
oneoftheninputsisdonebytheselected
inputs.Dependingonthedigitalcodeapplied
attheselectedinputs,oneoutofndata
sourcesisselectedandtransmittedtothe
singleoutputY.

17. Eiscalledthestrobeorenableinputwhichis
usefulforthecascading.Itisgenerallyan
activelowterminalthatmeansitwillperform
therequiredoperationwhenitislow.

18. Multiplexers come in multiple variations
•2 : 1 multiplexer
•4 : 1 multiplexer
•8 :1 multiplexer
•16 : 1 multiplexer
•32 : 1 multiplexer

19. Block Diagram Truth table

20. Block Diagram
Circuit Diagram

21. •Demultiplexers
•Ademultiplexerperformsthereverse
operationofamultiplexeri.e.itreceivesone
inputanddistributesitoverseveraloutputs.It
hasonlyoneinput,noutputs,mselectinput.
Atatimeonlyoneoutputlineisselectedby
theselectlinesandtheinputistransmittedto
theselectedoutputline.Ade-multiplexeris
equivalenttoasinglepolemultiplewayswitch
asshowninfig.

22. Demultiplexers comes in multiple variations.
•1 : 2 demultiplexer
•1 : 4 demultiplexer
•1 : 8 demultiplexer
•1 : 16 demultiplexer
•1 : 32 demultiplexer

23. Block Diagram Truth table
S

24. Block Diagram
Truth table
Circuit Diagram

25. Encoder
•Encoder is a combinational circuit which is
designed to perform the inverse operation of
the decoder.
•An encoder has n number of input lines and m
number of output lines.
•An encoder produces an m bit binary code
corresponding to the digital input number.
•The encoder accepts an n input digital word
and converts it into an m bit another digital
word.

26. Examples of Encoders are following.
•Priority encoders
•Decimal to BCD encoder
•Octal to binary encoder
•Hexadecimal to binary encoder
Block diagram

27. Priority encoder
4:2 Encoder Circuit

28. Block Diagram Truth Table Circuit Diagram

29. Decoder
Adecoderisacombinationalcircuit.Ithasn
inputandproducemoutputs.(i.en=2m
output)Decoderisidenticaltoademultiplexer
withoutanydatainput.Itperformsoperations
whichareexactlyoppositetothoseofan
encoder.
Examples of Decoders are following.
•Code converters
•BCD to seven segment decoders
•Relay actuator

30. 2 to 4 Line Decoder
Theblockdiagramof2to4linedecoderis
showninthefig.AandBarethetwoinputs
whereDthroughDarethefouroutputs.Truth
tableexplainstheoperationsofadecoder.It
showsthateachoutputis1foronlyaspecific
combinationofinputs.
Block diagram
Basic Block

31. Logic Circuit
Truth Table