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Digital Logic & Design (DLD) presentation
- 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 BasicCombinationalBasic 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
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- 14. Combinational Logic 14 4-bitAdder 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 BinarySubtractorBinary 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-BitAdder and Subtractor4-Bit Adder and Subtractor )( )(1 )(0 OverflowV SubtractorM AdderM = = From course book
- 18. Combinational Logic 18 BinaryMultiplierBinary 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 Fromcourse 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 2x4Decoder2x4 Decoder
- 23. Combinational Logic 23 InternalStructure of 2x4Internal Structure of 2x4 DecoderDecoder
- 24. Combinational Logic 24 AnotherViewAnother View
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- 27. Combinational Logic 27 4x16Decoder4x16 Decoder From course book
- 28. Combinational Logic 28 FullAdder 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 2x1Multiplexer2x1 Multiplexer
- 31. Combinational Logic 31 4x1Multiplexer4x1 Multiplexer
- 32. Combinational Logic 32 BooleanFunctionBoolean Function ImplementationImplementation How do you implement it with 8x1 MUX?
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- 34. Combinational Logic 34 Three-StateBufferThree-State Buffer
- 35. Combinational Logic 35 2x1MUX 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 StudyProblemStudy 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 StudyProblemStudy 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 StudyProblemsStudy 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
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