Activity 2.1.3 AOI Logic Implementation
Introduction
Would you pay $199 for a written specification for an MP3 player? Would you pay $299 for
the schematics for a cell phone? Of course not. You don’t pay for the specifications or the
schematics; you pay for the product itself.
You are not quite to the point where you can design an MP3 player or a cell phone, but you
can design AOI logic circuits. In this activity you will learn how to implement AOI logic circuits
from logic expressions. The logic expressions will be in either Sum-Of-Products (SOP) or
Product-Of-Sums (POS) form.
Equipment




Circuit Design Software (CDS)
Breadboard
#22 Gauge solid wire
Integrated Circuits (74LS04, 74LS08, 74LS32)
Procedure
Let’s examine the process of implementing an AOI logic circuit by designing a circuit for the
relatively simple Sum-Of-Products (SOP) logic expression F1.
F1  A C  A C  A B C
1. In the space provided, draw an AOI circuit that implements the logic expression F 1. For
this implementation you may assume that AND & OR gates are available with any number
of inputs.
© 2014 Project Lead The Way, Inc.
Digital Electronics Activity 2.1.3 AOI Logic Implementation – Page 1
VCC
5V
S1
U1
U4
NOT
Key = A
U2
S2
X1
AND2
2.5 V
U7
U5
NOT
OR3
AND2
Key = B
U3
S3
U6
NOT
AND3
Key = C
GND
F1 – I
2. Re-implement the circuit assuming that only 2-input AND gates (74LS08), 2-input OR
gates (74LS32), and inverters (74LS04) are available. Draw this circuit in the space
provided.
VCC
5V
S1
U1
NOT
Key = A
S2
U2
U4
U8
X1
U6
AND2
2.5 V
AND2
U5
OR2
NOT
U7
U10
AND2
Key = B
OR2
S3
U3
OR2
U9
NOT
Key = C
AND2
GND
F1 – II
© 2014 Project Lead The Way, Inc.
Digital Electronics Activity 2.1.3 AOI Logic Implementation – Page 2
3. Using the CDS, enter and test the logic circuit that you designed. Use switches for the
inputs A, B, & C and a probe or LED circuit for the output F1. Verify that the circuit is
working as expected. Print a copy of the circuit and attach below.
VCC
5V
S1
U1
NOT
Key = A
S2
U2
U4
U8
AND2
2.5 V
AND2
U5
OR2
NOT
U7
U10
AND2
Key = B
X1
U6
OR2
S3
U3
OR2
U9
NOT
Key = C
AND2
GND
F1 – CDS
4. Using the DLB, build and test the logic circuit that you designed and simulated. Verify that
the circuit is working as expected and the results match the results of the simulation.
Though they are less frequently used, in later activities we will see that occasionally, logic
expression in the Product-Of-Sums (POS) form are easier to implement than SOP equations.
For practice let’s implement an AOI circuit for the logic expression F2.
F2  ( A  C )  ( A  B  C )
5. In the space provided, draw an AOI circuit that implements the logic expression F2. For
this implementation you may assume that AND & OR gates are available with any number
of inputs.
© 2014 Project Lead The Way, Inc.
Digital Electronics Activity 2.1.3 AOI Logic Implementation – Page 3
F2 – I
6. Re-implement the circuit assuming that only 2-input AND gates (74LS08), 2-input OR
gates (74LS32), and inverters (74LS04) are available. Draw this circuit in the space
provided.
F2 – II
7. Using the CDS, enter and test the logic circuit that you designed. Use switches for the
inputs A, B, & C and a probe or LED circuit for the output F2. Verify that the circuit is
working as expected. Print a copy of the circuit and attach below.
VCC
5V
X1
S1
U1
U4
2.5 V
U8
NOT
OR2
Key = A
S2
U2
NOT
AND2
U5
U7
OR2
OR2
Key = B
S3
U3
U6
NOT
OR2
Key = C
F2 – CDS
Conclusion
1. The two circuits shown below are equivalent, meaning that they both produce the same
output, Minterm=WXYZ.
© 2014 Project Lead The Way, Inc.
Digital Electronics Activity 2.1.3 AOI Logic Implementation – Page 4
Analyze each circuit to prove that they both produce the output Minterm=WXYZ.
Since the two versions produce the same output and require the same number of gates to
implement, is one version any better than the other?
Version 2 is better than version 1 because it will take more time for the signal to get by 3
gates than just 2 .
Note: Think delays. Though we don’t normally worry about it in our designs, remember that
all logic gates have propagation delay.
2. Shown below are two equivalent circuits. One was implemented from an SOP logic
expression and the other from the equivalent POS form.
First analyze the SOP version to determine the logic expression for F3 in SOP form. Use
this expression to generate a truth table for the circuit.
F3= A’B+B’C
A
B
C
F3
0
0
0
0
0
0
1
1
0
1
0
1
0
1
1
1
1
0
0
0
© 2014 Project Lead The Way, Inc.
Digital Electronics Activity 2.1.3 AOI Logic Implementation – Page 5
1
0
1
1
1
1
0
0
1
1
1
0
Now analyze the POS version to determine the logic expression for F3 in POS form. Use
this expression to generate a truth table for the circuit.
F3= (A’+B’)(B+C)
A
B
C
F3
0
0
0
0
0
0
1
1
0
1
0
1
0
1
1
1
1
0
0
0
1
0
1
1
1
1
0
0
1
1
1
0
How do the two truth tables compare? Is the column for F3 the same for both? Yes, since
the only difference is that the product of sums is not yet multiplied and once it is it come
out to the same as the sum of products.They should be. If they are not the same, review
your work and make any necessary corrections.
Since the truth tables are the same for F3, what could be said about the two logic
expressions? The logic Expressions are equal but not Identical, the answer still comes
out the same.
© 2014 Project Lead The Way, Inc.
Digital Electronics Activity 2.1.3 AOI Logic Implementation – Page 6