Digital Logic & Design (DLD) Prepared By:Md Foyez Ahammad. Email:foyezahammad@gmail.com or foyezbijoy@ gmail.com

1. DIGITAL LOGIC & DESIGNDIGITAL LOGIC & DESIGN
 PRESENTED BY:PRESENTED BY:
 Md. Foyez AhammadMd. Foyez Ahammad
 Dept: EEEDept: EEE
 ID:13205100ID:13205100
 PRESENTED FOR:PRESENTED FOR:
 Dr. Shariful IslamDr. Shariful Islam
 Faculty,Dept of EEEFaculty,Dept of EEE
Combinational Logic 1

2. Combinational Logic 2
RememberRemember
 CombinationalCombinational
 The outputs depend only on the current inputThe outputs depend only on the current input
valuesvalues
 It uses only logic gatesIt uses only logic gates
 SequentialSequential
 The outputs depend on the current and past inputThe outputs depend on the current and past input
valuesvalues
 It uses logic gates and storage elementsIt uses logic gates and storage elements
Network
.
.
.
.
.
.
Inputs Outputs

3. Combinational Logic 3
NotesNotes
 If there areIf there are nn input variables, there areinput variables, there are
2^n input combinations2^n input combinations
 For each input combination, there isFor each input combination, there is
one output valueone output value
 Truth tables are used to list allTruth tables are used to list all
possible combinations of inputs andpossible combinations of inputs and
corresponding output valuescorresponding output values

4. Combinational Logic 4
Basic CombinationalBasic Combinational
CircuitsCircuits
 AddersAdders
 MultipliersMultipliers
 MultiplexersMultiplexers
 DecodersDecoders
 EncodersEncoders
 ComparatorsComparators
 SubtractorsSubtractors

5. Combinational Logic 5
DesignDesign
 Determine the inputs and outputsDetermine the inputs and outputs
 Assign a symbol for eachAssign a symbol for each
 Derive the truth tableDerive the truth table
 Get the simplified boolean expressionGet the simplified boolean expression
for each outputfor each output
 Draw the network diagramDraw the network diagram

6. Combinational Logic 6
ExampleExample
 Conversion from BCD to excess-5Conversion from BCD to excess-5

7. Combinational Logic 7
Example (Cont.)Example (Cont.)
CDBAW ++=

8. Combinational Logic 8
Example (Cont.)Example (Cont.)
'''' BCDCBDBAX +++=

9. Combinational Logic 9
Example (Cont.)Example (Cont.)
diagramnetworktheDraw
ZandFindY

10. Combinational Logic 10
AddersAdders
 Essential part of every CPUEssential part of every CPU
 Half adder (Ignore the carry-in bit)Half adder (Ignore the carry-in bit)
 It performs the addition of two bitsIt performs the addition of two bits
 Full adderFull adder
 It performs the addition of three bitsIt performs the addition of three bits

11. Combinational Logic 11
Half-AdderHalf-Adder
 You can use K-Map to simplifyYou can use K-Map to simplify
 It is also obvious from the truth tableIt is also obvious from the truth table

12. Combinational Logic 12
Full-AdderFull-Adder

13. Combinational Logic 13
Full-AdderFull-Adder
iiiiiiiii
iiii
BACBACBAC
CBAS
++=
⊕⊕=
+ ''1
HOW?????

14. Combinational Logic 14
4-bit Adder Implementation4-bit Adder Implementation
From course book
00 =C

15. Combinational Logic 15
QuestionQuestion
 How can you get 32-bit implementation?How can you get 32-bit implementation?

16. Combinational Logic 16
Binary SubtractorBinary Subtractor
 RememberRemember
 You need to take 2’s complement to representYou need to take 2’s complement to represent
negative numbersnegative numbers
 A-BA-B
 Take 2’s complement of B and add it to ATake 2’s complement of B and add it to A
 First take 1’s complement and add 1First take 1’s complement and add 1

17. Combinational Logic 17
4-Bit Adder and Subtractor4-Bit Adder and Subtractor
)(
)(1
)(0
OverflowV
SubtractorM
AdderM
=
=
From course book

18. Combinational Logic 18
Binary MultiplierBinary Multiplier
From course book

19. Combinational Logic 19
ComparatorsComparators
 Compare two input wordsCompare two input words
 Returns 1 ifReturns 1 if
A=B, 0A=B, 0
otherwiseotherwise

20. Combinational Logic 20
From course book

21. Combinational Logic 21
DecoderDecoder
 n by 2^n decodern by 2^n decoder
 Converts information from n input lines into 2^nConverts information from n input lines into 2^n
output linesoutput lines
 2x4 Decoder2x4 Decoder
 3x8 Decoder3x8 Decoder

22. Combinational Logic 22
2x4 Decoder2x4 Decoder

23. Combinational Logic 23
Internal Structure of 2x4Internal Structure of 2x4
DecoderDecoder

24. Combinational Logic 24
Another ViewAnother View

25. Combinational Logic 25
From
course
book

26. Combinational Logic 26
ExampleExample

27. Combinational Logic 27
4x16 Decoder4x16 Decoder
From course book

28. Combinational Logic 28
Full Adder with DecoderFull Adder with Decoder
iiiiiiiii
iiii
BACBACBAC
CBAS
++=
⊕⊕=
+ ''1

29. Combinational Logic 29
MultiplexersMultiplexers
 You can select information from one ofYou can select information from one of
many input lines and assign it to onemany input lines and assign it to one
output lineoutput line
 You have input lines, control lines, andYou have input lines, control lines, and
one output lineone output line
 It is called MUXIt is called MUX

30. Combinational Logic 30
2x1 Multiplexer2x1 Multiplexer

31. Combinational Logic 31
4x1 Multiplexer4x1 Multiplexer

32. Combinational Logic 32
Boolean FunctionBoolean Function
ImplementationImplementation
How do you implement it with 8x1 MUX?

33. Combinational Logic 33
ExampleExample

34. Combinational Logic 34
Three-State BufferThree-State Buffer

35. Combinational Logic 35
2x1 MUX with Three-State2x1 MUX with Three-State
BufferBuffer

36. Combinational Logic 36
ShiftersShifters
 8-input, 8-output shifter8-input, 8-output shifter
 C=1 => right shift, C=0 => left shiftC=1 => right shift, C=0 => left shift

37. Combinational Logic 37
Study ProblemStudy Problem
 Course Book Chapter – 4 ProblemsCourse Book Chapter – 4 Problems
 4 – 314 – 31
 Construct a 16x1 multiplexer with two 8x1 andConstruct a 16x1 multiplexer with two 8x1 and
one 2x1 multiplexer. Use block diagramsone 2x1 multiplexer. Use block diagrams

38. Combinational Logic 38
Study ProblemStudy Problem
 Course Book Chapter – 4 ProblemsCourse Book Chapter – 4 Problems
 4 – 344 – 34
implementsrmultiplexehat thefunction tBooleantheDetermine
'
;
;1
;0
inputsdataThe
ly.respectiveSand,S,Sinputsselectionthe
toconnectedCandB,A,inputshasrmultiplexe8x1An
6
40
53
721
012
DI
DII
II
III
=
==
==
===

39. Combinational Logic 39
Study ProblemsStudy Problems
 Course Book Chapter – 4 ProblemsCourse Book Chapter – 4 Problems
 4 – 14 – 1
 4 – 44 – 4
 4 – 64 – 6
 4 – 114 – 11
 4 – 204 – 20
 4 – 214 – 21
 4 – 254 – 25
 4 – 324 – 32
 4 – 334 – 33
 4 – 354 – 35

40. Combinational Logic 40
QuestionsQuestions