AOI Logic Analysis
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Digital Electronics
There are 2 ways to analyze
Truth Table → Equation Technique
Given A Logic Circuit . . .
• Extract truth table
• Derive logic expression
Equation → Truth Table Technique
These are 2
ways you
can analyze
a logic
circuit
Given A Logic Circuit . . .
• Extract logic expression
• Derive truth table
2
Truth Table → Equation Technique
The Process
a) Add test-points at the output of every gate.
b) Add a column to the truth table for every testpoint.
c) Working from the inputs to the output, complete
the truth table for each test-point, ultimately
ending at the circuit’s output.
d) From the completed truth table, identify the
Minterms from the truth table anywhere the output
is one.
e) Using the extracted Minterms, write the Sum-Of3
Products logic expression.
Truth Table → Equation
Process Walk-Thru
The next slides will show how to figure out the
logic expression for the output F1 .
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Truth Table → Equation
Process Walk-Thru : Step (a)
a) Add test-points at the output of every gate.
TP1
TP2
TP3
TP5
TP4
Write down what each test point really means on the drawing
TP1= X inverted = X
TP2= XY
TP3=XYZ
TP4=Y
TP5=XY
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Truth Table → Equation
Process Walk-Thru : Steps (b) & (c)
b) Add a column to the truth table for every test-point.
c) Working from the inputs to the output, complete the
truth table for each test-point, ultimately ending at
the circuit’s output. Notice that TP1 is exactly the opposite of X
X
Y
Z
F1
TP1
TP2
TP3
TP4
TP5
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
1
1
1
1
1
0
0
1
0
0
1
0
0
0
1
1
1
0
1
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
TP5 = X
and TP4
If both X
and TP4
are 1, then
TP5 is
also a 1
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Truth Table → Equation
Process Walk-Thru : Steps (d) & (e)
d) From the completed truth table, identify the Minterms
from the truth table anywhere the output is one.
X
Y
Z
F1
TP1
TP2
TP3
TP4
TP5
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
1
0
0
0
XY Z

0
1
1
1
1
1
1
0
0
X Y Z

1
0
0
1
0
0
0
1
1
X Y Z

1
0
1
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
Write
down the
equations
e) Using the extracted Minterms, write the Sum-OfProducts logic expression.
F1  X Y Z  X Y Z  X Y Z
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Example #1: Circuit Analysis
Example Here is another, do this one
Analyze the logic circuit shown below to
determine the circuit’s truth table. Using the
truth table, derive the logic expression for
the output F2.
You should try to solve this
yourself and fill in the next
slide BEFORE you look at
the answer coming up!
8
Example #1: Circuit Analysis
Solution
TP1
a)
TP2
TP3
TP4
TP5
b) & c)
d)
B
C
F2
TP1
TP2
TP3
TP5
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
XY Z

0
1
0
1
1
1
0
1
1
XY Z

0
1
1
1
1
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
1
1
1
0
0
0
0
0
0
XY Z
e)
e) TP4
A

F2  X Y Z  X Y Z  X Y Z
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Equation → Truth Table Technique
The Process This is the OTHER way to analyze circuits
a) Working from the inputs to the output, write
the cumulating logic expression at the
output of each gate concluding with the
expression for the circuit’s output.
b) Using the circuit’s output logic expression,
derive the circuit’s truth table.
10
Equation → Truth Table Technique
Process Walk-Thru
Analyze the logic circuit shown below to determine
the logic expression for the output F1. Using the
logic expression, derive the circuit’s truth table.
11
Equation → Truth Table Technique
Process Walk-Thru : Step (a)
a) Working from the inputs to the output, write the
cumulating logic expression at the output of each
gate concluding with the expression for the circuit’s
output.
X
XY
XY Z
Y
 XY Z XY
X Y
12
Equation → Truth Table Technique
Process Walk-Thru : Step (b)
b) Using the circuit’s output logic expression, derive
the circuit’s truth table.
F1  X Y Z  X Y
X
Y
Z
F1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
1
0
0
1
1
0
1
1
1
1
0
0
1
1
1
0

If you look at the picture of the
circuit you can write what the
equation is
XY Z
X Y
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Example #2: Circuit Analysis
Example
Analyze the logic circuit shown below to
determine the logic expression for the output
F1. Using the logic expression, derive the
circuit’s truth table.
Do this one
on your own
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