Activity 2.1.2 AOI Logic Analysis:
Circuit to Truth Table to Logic Expression
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.
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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Digital Electronics Activity 2.1.2 AOI Logic Analysis – Page 1
1. Using the test points that have been assigned (TP1-TP4), complete the following truth
table.
​X
Y
TP1
TP2
TP3
TP4
F1
0
0
1
0
1
0
0
0
1
0
0
1
1
1
1
0
1
1
0
0
1
1
1
0
0
0
0
0
2. Using the truth table, write out the Minterms for every location that contains a (1) in the
F1 column.
tp1’tp2’tp3tp4
3. Using the Minterm(s), write the logic expression for the output F1.
tp1’tp2’tp3tp4 + tp1tp2tp3’tp4’
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.
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Digital Electronics Activity 2.1.2 AOI Logic Analysis – Page 2
4. Using the circuit diagram below, write the logic expression at the output of each gate
until you reach the output of the circuit.
A = y’
B = ‘x
C = xy’
D = x’y
F1 = xy’ + x’y
5. Using the logic expression, complete the truth table shown below.
X
Y
F1
0
0
0
0
1
1
1
0
1
1
1
0
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.
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Digital Electronics Activity 2.1.2 AOI Logic Analysis – Page 3
Let’s analyze a more complex circuit. Complete the following steps for the three input AOI
logic diagram shown below.
6. 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.
R
S
T
F2
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
1
1
0
1
1
1
1
0
1
1
1
1
1
1
0
F2 = r’st’ + rs’t’ + rs’t + rst’ + rst
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Digital Electronics Activity 2.1.2 AOI Logic Analysis – Page 4
7. 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
0
0
0
1
0
0
1
0
1
0
1
1
0
1
0
0
1
1
0
1
1
1
1
0
1
1
1
1
1
F2 = r’t’s + rst + rs’
8. 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.
They are the same on both tables.
9. How do the logic expressions obtained from the two techniques compare? Are they
the same?
The second one is significantly shorter and clearly more simplified that the latter.
They are clearly not the same.
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Digital Electronics Activity 2.1.2 AOI Logic Analysis – Page 5
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.
Using the logic gates that you are given, logic tables are created which can then be
put together to find the larger table of the final result table. This final table can give
the logic expression by looking at which of the outputs return true.
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.
By extracting the logic expression first from the graphic of the combined logic gates,
you can then try different combinations of inputs to find the truth table of the circuit.
3. Did you find one of the processes easier than the other? Which one and why?
I found the second one easier than the first. I can determine the expression quite
faster by just looking at the circuit that gets the tables and combining them and then
deriving the logic expression. Just because it was faster for me to do.
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Digital Electronics Activity 2.1.2 AOI Logic Analysis – Page 6
4. How can two logic equations that are not identical be equal or equivalent?
They can look different and be composed of different gates but return the same
outputs therefore making them equivalent.
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Digital Electronics Activity 2.1.2 AOI Logic Analysis – Page 7