chapter 4 analysis and design of combinational logic (sections 4.1 – 4.2)

CHAPTER 4CHAPTER 4Analysis and Design of Analysis and Design of Combinational LogicCombinational Logic

(Sections 4.1 – 4.2)(Sections 4.1 – 4.2)

Combinational CircuitsCombinational Circuits A combinational circuit consists of logic gates A combinational circuit consists of logic gates

whose outputs, at whose outputs, at any timeany time, are determined by , are determined by combining the values of the inputs.combining the values of the inputs.

For For nn input variables, there are 2 input variables, there are 2nn possible possible binary input combinations.binary input combinations.

For each binary combination of the input For each binary combination of the input variables, there is one possible binary value on variables, there is one possible binary value on each output.each output.

Combinational Circuits (cont.)Combinational Circuits (cont.) Hence, a combinational circuit can be described by:Hence, a combinational circuit can be described by:

CombinationalCircuit

.. ..x1x2

xn ym

y2

y1

y3

Y1=f1(x1,x2,…,xn)Y2=f2(x1,x2,…,xn)

Ym=fm(x1,x2,…,xn)...

Combinational vs. Sequential CircuitsCombinational vs. Sequential Circuits


n-inputs m-outputs(Depend only on inputs)


n-inputs

m-outputsStorageElementsNextstate

Presentstate

Sequential Circuit

Combinational Circuit

AnalysisAnalysis of Combinational Logic of Combinational Logic

Deriving Switching EquationsDeriving Switching Equations Simplifying the switching equationsSimplifying the switching equations Giving truth tableGiving truth table Logic function conclussionLogic function conclussion

E.g. Analysis the functionality of the following E.g. Analysis the functionality of the following circuitcircuit


&

≥1≥1

&

A

B

YP1

P2

P3

Y=(A’+B’)A+(A’+B’)B=A’B+AB’

Y=A⊕B


E.g. Analysis the functionality of the E.g. Analysis the functionality of the following circuitfollowing circuit P1=(ABC)’

P2=A·P1=A·(ABC)’P3=B·P1=B·(ABC)’P4=C·P1=C·(ABC)’

F=(P2+P3+P4)’=(A·(ABC)’+B·(ABC)’+C·(ABC)’)’=((ABC)’(A+B+C))’=ABC+A’B’C’


Giving truth tableGiving truth table

Logic function conclussionLogic function conclussion

Combinational Circuit Combinational Circuit DesignDesign DesignDesign of a combinational circuit is the of a combinational circuit is the

development of a circuit from a description of development of a circuit from a description of its function.its function.

Starts with a problem specification and Starts with a problem specification and produces a logic diagram or set of boolean produces a logic diagram or set of boolean equations that represent the circuit.equations that represent the circuit.

Combinational Circuit Combinational Circuit DesignDesign1.1. Determine the required number of inputs and Determine the required number of inputs and

outputs and assign variables to them.outputs and assign variables to them.2.2. Derive the truth table that defines the required Derive the truth table that defines the required

relationship between inputs and outputs.relationship between inputs and outputs.3.3. Obtain and Obtain and simplifysimplify the Boolean function (K-maps, the Boolean function (K-maps,

algebraic manipulation, CAD tools, …). Consider algebraic manipulation, CAD tools, …). Consider any design constraints (area, delay, power, available any design constraints (area, delay, power, available libraries, etc).libraries, etc).

4.4. Draw the logic diagram.Draw the logic diagram.5.5. VerifyVerify the correctness of the design. the correctness of the design.

E.g1. Design a combinational circuit that will E.g1. Design a combinational circuit that will multiply two two-bit binary valuesmultiply two two-bit binary values

Solution:Solution:1. input variables(A1. input variables(A11,A,A00,B,B11,B,B00))

output variables(Poutput variables(P33,P,P22,P,P11,P,P00))

Combinational Circuit Combinational Circuit DesignDesign

2. Construct a truth table 2. Construct a truth table


P3=f(A1,A0,B1,B0)=∑(15)P2=f(A1,A0,B1,B0)=∑(10,11,14)P1=f(A1,A0,B1,B0)=∑(6,7,9,11,13,14)P0=f(A1,A0,B1,B0)=∑(5,7,13,15)

The output SOP equations The output SOP equations are:are:

3. The individually 3. The individually simplified equations simplified equations areare

PP33=A=A11AA00BB11BB00

PP22=A=A11AA00’B’B11+A+A11BB11BB00’’

PP11=A=A11’A’A00BB11+A+A00BB11BB00’+A’+A11BB11’B’B00++AA11AA00’B’B00

PP00=A=A00BB00


Combinational Circuit Combinational Circuit DesignDesign E.g.2 E.g.2 Design a combinational circuit that will accept a Design a combinational circuit that will accept a

2421BCD code and drive a TIL-312 seven-segment display2421BCD code and drive a TIL-312 seven-segment display

A GFEDCB



TRUTH TABLE


A=∑(1,10)B=∑(11,12)C=∑(8)D=∑(1,10,13)E=∑(1,9,10,11,13,15)F=∑(1,8,9,13)G=∑(0,1,13)

A=w’z+x’yz’B=xy’z’+x’yzC=wx’y’z’D=xy’z+x’yz’+w’zE=x’y+zF=wx’y’+y’zG=w’+xy’z

A=[(w’z)’(x’yz’)]’B=[(xy’z’)’(x’yz)’]C=(wx’y’z’)’’D=[(xy’z)’(x’yz’)’(w’z)’]’E=[(x’y)’(z)’]’F=[(wx’y’)’(y’z)’]’G=[(w)(xy’z)’]’

4.2 Introduction to Digital IC4.2 Introduction to Digital IC IC package introductionIC package introduction IC categoryIC category

TTLTTLECLECLCMOSCMOS

Low power(L)High speed(H)Low power Schottky(LS)Schottky(S)Advanced Low power Schottky(ALS)Advanced Schottky(AS)

IC naming regulationIC naming regulation

4.2 Introduction to Digital IC4.2 Introduction to Digital IC

SN74LS00SN74LS00

manufacture54--- military operating temperature range74--- commercial temperature range

Low power(L)High speed(H)Low power Schottky(LS)Schottky(S)Advanced Low power Schottky(ALS)Advanced Schottky(AS)

4.2 Introduction to Digital IC4.2 Introduction to Digital IC

Exe.Exe.

chapter 4 analysis and design of combinational logic (sections 4.1 – 4.2)

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