Combinational Logic 1

DIGITAL LOGIC DESIGN

by

Dr. Fenghui Yao

Tennessee State University

Department of Computer Science

Nashville, TN

Combinational Logic 2

RememberRemember

CombinationalCombinational The outputs depend only on the current input The outputs depend only on the current input

valuesvalues It uses only logic gatesIt uses only logic gates

Sequential Sequential The outputs depend on the current and past input The outputs depend on the current and past input

valuesvalues It uses logic gates and storage elementsIt uses logic gates and storage elements

Network.

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Inputs Outputs

Combinational Logic 3

NotesNotes

If there are If there are n n input variables, there are input variables, there are 2^n input combinations2^n input combinations

For each input combination, there is For each input combination, there is one output valueone output value

Truth tables are used to list all Truth tables are used to list all possible combinations of inputs and possible combinations of inputs and corresponding output values corresponding output values

Combinational Logic 4

Basic Combinational Basic Combinational CircuitsCircuits AddersAdders MultipliersMultipliers MultiplexersMultiplexers DecodersDecoders EncodersEncoders ComparatorsComparators SubtractorsSubtractors

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 expression Get the simplified boolean expression

for each outputfor each output Draw the network diagramDraw the network diagram

Combinational Logic 6

ExampleExample

Conversion from BCD to excess-5Conversion from BCD to excess-5

Combinational Logic 7

Example (Cont.)Example (Cont.)

CDBAW

Combinational Logic 8

Example (Cont.)Example (Cont.)

'''' BCDCBDBAX

Combinational Logic 9

Example (Cont.)Example (Cont.)

diagramnetwork theDraw

Zand FindY

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

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

Combinational Logic 12

Full-AdderFull-Adder

Combinational Logic 13

Full-AdderFull-Adder

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BACBACBAC

CBAS

''1

HOW?????

Combinational Logic 14

4-bit Adder Implementation4-bit Adder ImplementationFrom course book

00 C

Combinational Logic 15

QuestionQuestion

How can you get 32-bit implementation?How can you get 32-bit implementation?

Combinational Logic 16

Binary SubtractorBinary Subtractor

RememberRemember You need to take 2’s complement to represent You 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

Combinational Logic 17

4-Bit Adder and Subtractor4-Bit Adder and Subtractor

)(

)(1

)(0

OverflowV

SubtractorM

AdderM

From course book

Combinational Logic 18

Binary MultiplierBinary Multiplier

From course book

Combinational Logic 19

ComparatorsComparators Compare two input wordsCompare two input words

Returns 1 if Returns 1 if A=B, 0 A=B, 0 otherwiseotherwise

Combinational Logic 20From course book

Combinational Logic 21

DecoderDecoder

n by 2^n decoder n by 2^n decoder Converts information from n input lines into 2^n Converts information from n input lines into 2^n

output linesoutput lines

2x4 Decoder2x4 Decoder 3x8 Decoder3x8 Decoder

Combinational Logic 22

2x4 Decoder2x4 Decoder

Combinational Logic 23

Internal Structure of 2x4 Internal Structure of 2x4 Decoder Decoder

Combinational Logic 24

Another View Another View

Combinational Logic 25

From course book

Combinational Logic 26

ExampleExample

Combinational Logic 27

4x16 Decoder4x16 Decoder

From course book

Combinational Logic 28

Full Adder with DecoderFull Adder with Decoder

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iiii

BACBACBAC

CBAS

''1

Combinational Logic 29

MultiplexersMultiplexers

You can select information from one of You can select information from one of many input lines and assign it to one many input lines and assign it to one output lineoutput line

You have input lines, control lines, and You have input lines, control lines, and one output lineone output line

It is called MUXIt is called MUX

Combinational Logic 30

2x1 Multiplexer2x1 Multiplexer

Combinational Logic 31

4x1 Multiplexer4x1 Multiplexer

Combinational Logic 32

Boolean Function Boolean Function ImplementationImplementation

How do you implement it with 8x1 MUX?

Combinational Logic 33

ExampleExample

Combinational Logic 34

Three-State BufferThree-State Buffer

Combinational Logic 35

2x1 MUX with Three-State 2x1 MUX with Three-State BufferBuffer

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

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 and Construct a 16x1 multiplexer with two 8x1 and

one 2x1 multiplexer. Use block diagramsone 2x1 multiplexer. Use block diagrams

Combinational Logic 38

Study ProblemStudy Problem

Course Book Chapter – 4 ProblemsCourse Book Chapter – 4 Problems 4 – 344 – 34

implementsr multiplexe hat thefunction tBoolean theDetermine

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inputs data The

ly.respective S and ,S ,S inputsselection the

toconnected C and B, A, inputs hasr multiplexe 8x1An

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40

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721

012

DI

DII

II

III

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

Combinational Logic 40

QuestionsQuestions