# 2 1 2 ```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.
1. Using the assigned test points (TP1–TP4), complete the following truth table.
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Activity 2.1.2 AOI Logic Analysis: Circuit to Truth Table to Logic Expression
X
0
0
1
1
Y
0
1
0
1
F1
0
1
1
0
TP1
1
0
1
0
TP2
0
0
1
0
TP3
1
1
0
0
TP4
0
1
0
0
2. Using the truth table, write out the Minterms for every location that contains a (1) in the F1
TP1’TP2’TP3TP4
TP1TP2TP3’TP4’
3. Using the Minterms, write the logic expression for the output F1 in your notebook.
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.
4. Using the circuit diagram below, write the logic expression at the output of each gate until you
reach the output of the circuit.
F1=XY=XY
5. Using the logic expression, complete the truth table below.
X
0
0
1
1
Y
0
1
0
1
F1
0
1
1
0
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Activity 2.1.2 AOI Logic Analysis: Circuit to Truth Table to Logic Expression
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.
Obtaning from the second technique was much easier, the result is the same
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
0
0
0
0
1
1
1
1
S
0
0
1
1
0
0
1
0
T
0
1
0
1
0
1
0
1
F2
0
0
1
0
1
1
1
1
F2 =R’ST+RS’T+RS’T+RST’+RST
7. 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 F2 = R’T’S+RST+RS’
0
0
0
0
1
1
1
1
0
0
1
1
0
0
1
0
0
1
0
1
0
1
0
1
0
0
1
0
1
1
1
1
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Activity 2.1.2 AOI Logic Analysis: Circuit to Truth Table to Logic Expression
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.
The labels are the same
9. How do the logic expressions obtained from the two techniques compare? Are they the same?
The circuit is smaller compared to the one from the un-simplified
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```