Digital Electronics 4

8/12/2019 Digital Electronics 4

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Circui t Analys is Procedure

by

Dr.M.ManikandanAssociate Professor

Dep t. o f Elec tron ics Engg .Anna Un iversi ty.


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Overview

Important concept analyze digital

circuits

Given a circuit

Create a truth table

Create a minimized circuit


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Overview

Approaches Boolean expression approach

Truth table approach Leads to minimized hardware

Provides insights on how to design

hardware


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The Problem

How can we convert from a circuitdrawing to an equation or truth

table?

Two approaches

Create intermediate equations

Create intermediate truth tables


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The Problem

A

BC

A

B

C

Out


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Label Gate Outputs

Label all gate outputs that are afunction of input variables.

Label gates that are a function ofinput variables and previously

labeled gates.

Repeat process until all outputs are

labelled.


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Label Gate Outputs

C

A

B

C

A

B

Out

R

S

T


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Approach 1: Create

Intermediate EquationsStep 1: Create an equation for each

gate output based on its input.

R = ABC

S = A + B

T = CS

Out = R + T


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Approach 1: Create

Intermediate Equations

A

B

C

A

B

C

Out

R

S

T


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Approach 1: Substitute in

subexpressions Step 2: Form a relationship based on input

variables (A, B, C)

R = ABC

S = A + B

T = CS = C(A + B)

Out = R+T = ABC + C(A+B)


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Approach 1: Substitute

in subexpressionsAB

C

A

B

C

Out

R

S

T


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Approach 1: Substitute in

subexpressions Step 3: Expand equation to SOP

final result

Out = ABC + C(A+B) = ABC +

AC + BC

Out


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Approach 1: Substitute

in subexpressions

A

C

Out

B

C

AB

C


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Approach 2: Truth Table

Step 1: Determine outputs forfunctions of input variables.

A0000

1111

B0011

0011

C0101

0101

R0000

0001

S0011

1111


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AB

C

A

B

C

Out

R

S

T


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Step 2: Determine outputs for

functions of intermediate variables.

T = S * C

A000

0111

1

B001

1001

1

C010

1010

1

R000

0000

1

S001

1111

1

T001

0101

0

C101

0101

0


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A

BC

A

B

C

Out

R

S

T


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Step 3: Determine outputs for function.

A

0000

1111

B

0011

0011

C

0101

0101

R

0000

0001

S

0011

1111

T

0010

1010

Out

0010

1011

R + T = Out


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ABC

A

B

C

Out

R

S

T


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More Difficult Example

Step 3: Note labels on interior nodes

Logic Diagram for Analysis Example


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More Difficult Example: Truth

Table Remember to determine

intermediate variables starting from

the inputs.

When all inputs determined for a

gate, determine output.

The truth table can be reduced

using K-maps.


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More Difficult Example: Truth

Table

A00001111

B00110011

C01010101

F200010111

F21

1101000

T10

1111111

T20

0000001

T30

1101000

F10

1101001


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Summary

Important to be able to convertcircuits into truth table and

equation formWHY? ---- leads to minimized

sum of productrepresentation


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Summary

Two approaches illustrated Approach 1: Create an

equation with circuit output

dependent on circuit inputs

Approach 2: Create a truth

table which showsrelationship between circuit

inputs and circuit outputs


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Summary

Both results can then be

minimized using K-maps. Next time: develop a minimized

SOP representation from a highlevel description

Digital Electronics 4

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