engin 112 intro to electrical and computer engineering lecture 12 circuit analysis procedure n.
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ENGIN 112 Intro to Electrical and Computer Engineering Lecture 12 Circuit Analysis Procedure. Overview. Important concept – analyze digital circuits Given a circuit Create a truth table Create a minimized circuit Approaches Boolean expression approach Truth table approach

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overview
Overview
  • Important concept – analyze digital circuits
    • Given a circuit
      • Create a truth table
      • Create a minimized circuit
  • Approaches
    • Boolean expression approach
    • Truth table approach
  • Leads to minimized hardware
  • Provides insights on how to design hardware
    • Tie in with K-maps (next time)
the problem

A

B

C

Out

A

B

C’

The Problem
  • How can we convert from a circuit drawing to an equation or truth table?
  • Two approaches
    • Create intermediate equations
    • Create intermediate truth tables
label gate outputs

A

B

R

C

Out

T

S

A

B

C’

Label Gate Outputs
  • Label all gate outputs that are a function of input variables.
  • Label gates that are a function of input variables and previously labeled gates.
  • Repeat process until all outputs are labelled.
approach 1 create intermediate equations

A

B

R

C

Out

T

S

A

B

C’

Approach 1: Create Intermediate Equations
  • Step 1: Create an equation for each gate output based on its input.
    • R = ABC
    • S = A + B
    • T = C’S
    • Out = R + T
approach 1 substitute in subexpressions

A

B

R

C

Out

T

S

A

B

C’

Approach 1: Substitute in subexpressions
  • Step 2: Form a relationship based on input variables (A, B, C)
    • R = ABC
    • S = A + B
    • T = C’S = C’(A + B)
    • Out = R+T = ABC + C’(A+B)
approach 1 substitute in subexpressions1

A

B

A

B

C’

C’

Approach 1: Substitute in subexpressions
  • Step 3: Expand equation to SOP final result
    • Out = ABC + C’(A+B) = ABC + AC’ + BC’

C

Out

approach 2 truth table

A

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B

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R

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Out

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C’

Approach 2: Truth Table
  • Step 1: Determine outputs for functions of input variables.
approach 2 truth table1

A

B

C’

1

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R

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Approach 2: Truth Table
  • Step 2: Determine outputs for functions of intermediate variables.

A

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T = S * C’

approach 2 truth table2

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B

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Out

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R

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Out

T

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C’

Approach 2: Truth Table
  • Step 3: Determine outputs for function.

R + T = Out

more difficult example
More Difficult Example
  • Step 3: Note labels on interior nodes
more difficult example truth table

F2

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0

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1

F’2

1

1

1

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1

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T1

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T2

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T3

0

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F1

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1

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.

A

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summary
Summary
  • Important to be able to convert circuits into truth table and equation form
    • WHY? ---- leads to minimized sum of product representation
  • Two approaches illustrated
    • Approach 1: Create an equation with circuit output dependent on circuit inputs
    • Approach 2: Create a truth table which shows relationship between circuit inputs and circuit outputs
  • Both results can then be minimized using K-maps.
  • Next time: develop a minimized SOP representation from a high level description