Activity 2.1.4 AOI Logic Analysis
Introduction
What does this circuit do? Does the circuit that I designed work? If you are able to
analyze AOI logic circuits, you will be able to answer these questions. The first
question frequently comes up when you need to determine the functionality of a
previously designed circuit. The second question will always need to be answered
whenever you design a new logic circuit.
When you analyze an AOI logic circuit, you can use one of two techniques. With the
first technique, you determine the circuit’s truth table from which the output logic
expression is derived. With the second technique, the order is reversed. The circuit’s
logic expression is determined. The truth table is then derived using this expression.
In this activity you will learn how to analyze AOI logic circuits to determine the circuit
truth table and output logic expression.
Equipment


Paper and Pencil
Calculator
Procedure
Let’s start by analyzing the relatively simple AOI logic circuit shown below. You will
use the technique where you first extract the truth table and then use the truth table
to derive the output’s logic expression.
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1. Using the test points that have been assigned (TP1-TP4), complete the following
truth table.
TP1
TP2
TP4
TP3
X
Y
F1
TP1
TP2
TP3
TP4
0
0
0
1
0
1
0
0
1
1
1
1
0
1
1
0
1
0
1
1
1
1
1
1
0
1
0
1
2. Using the truth table, write out the Minterms for every location that contains a (1)
in the F1 column.
F1=X’Y+XY’+XY
3. Using the Minterm(s), write the logic expression for the output F1.
F1=X’Y+XY’+XY
Re-analyze the simple AOI logic circuit using the technique where you first extract the
logic expression for the output and then use the logic expression to derive the truth
table.
1. Using the circuit diagram below, write the logic expression at the output of each
gate until you reach the output of the circuit.
F1=X’Y’+XY’+X’Y+XY
2. Using the logic expression, complete the truth table shown below.
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X
Y
F1
0
0
0
0
1
1
1
0
1
1
1
1
How do the logic expressions and truth tables obtained from the two techniques
compare? Are they the same? They should be. If they are not, review your work
and correct any mistakes.
Let’s analyze a more complex circuit. Complete the following steps for the three
input AOI logic diagram shown below.
1. Using the analysis technique where you first extract the truth table and then use
it to derive the output’s logic expression, analyze the circuit. Record your results
below.
F2=R’ST’+R’S’T’+R’ST+RST’
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R
S
T
F2
0
0
0
1
0
0
1
0
0
1
0
1
0
1
1
1
1
0
0
0
1
0
1
0
1
1
0
1
1
1
1
0
F2 = R’ST’+R’S’T’+R’ST+RST’
2. Now, using the analysis technique where you first extract the logic expression for
the output and then use it to derive the truth table, analyze the circuit. Record
your results below.
R
S
T
F2
0
0
0
1
0
0
1
0
0
1
0
1
0
1
1
1
1
0
0
0
1
0
1
0
1
1
0
1
1
1
1
0
F2 = R’ST’+R’S’T’+R’ST+RST’
3. How do the truth tables obtained from the two techniques compare? Are they the
same? They should be. If they are not, review your work and correct any
mistakes.
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4. How do the logic expressions obtained from the two techniques compare? Are
they the same?
All answers had matched accurately between the two techniques. They are not
the same but equal to one another
They are NOT the SAME, but they are EQUAL. In later activities we will learn
how to use Boolean algebra to simplify logic expressions like these and prove
that they are equal.
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Conclusion
1. In your own words, describe the process used to analyze a logic circuit where
you first extract a truth table and then derive the logic expression.
First off you must look at the types of switches found within the circuit. Then
according to the type of switch found within a circuit you can derive weather or
not the given circuit will be a 0 or a 1 (on or off positions) Then based upon the
combination of 1’s and 0’s you can figure out whether the output at the end of the
circuit will become toggled. Then through this process of trial and order you can
begin formulating a Truth Table and thus through filling this table out you can
piece together a logical expression for a given circuit.
2. Again, in your own words, describe the process used to analyze a logic circuit
where you first extract the logic expression and then derive the truth table.
First off you must look at the types of switches found within the circuit. Then
according to the type of switch found within a circuit you can derive whether or
not the given circuit will be a 0 or a 1 (on or off positions) Then based upon the
combination of 1’s and 0’s you can figure out whether the output at the end of the
circuit will become toggled. Then through this process of trial and order you can
begin formulating a Truth Table and thus through filling this table out you can
piece together a logical expression for a given circuit.
3. Did you find one of the processes easier than the other? Which one and why?
I found the 2nd method to be easiest due to the monitoring of different outputs as well
as the generalized form of the 1st method. Not having to keep track of TP1, TP2, etc
makes life a whole lot easier.
4. What is the difference between two logic equations being equal versus two logic
equations being equivalent?
By equal it means that they are the same. By equivalent it means that they consist of
different items or values but they add up to the same end sum or value
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