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Simplification of Boolean Functions
Experiment 3
Objective
To demonstrate the relationship between Boolean functions and the corresponding logic diagram.
Procedure
Logic Diagram
For this part of the experiment we are given a logic diagram that we must simplify and reduce
the number of gates, and possibly the number of ICs.
The logic diagram (Figure 3.1) is shown
below and requires two ICs – a 7400 and a 7410.
Pin numbers were assigned to all inputs and
outputs of the gates.
We then connected the circuits with the x, y, and z inputs going to three
switches and the output
F
to an indicator lamp.
We tested the circuit to obtain the truth table
below (Table 3.1).
Figure 3.1
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View Full DocumentTable 3.1
x
y
z
F
1
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
1
Once we had the truth table we were able to create a map to simplify the function
F
1
to get
F
2
.
The map is shown below (Map 3.1)
Map 3.1
x
yz
00
01
11
10
0
0
0
1
0
1
1
1
1
0
Using this map we determined that
F
2
= xy` + yz.
Using DeMorgan’s Theorem we converted
this function to
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 Spring '08
 lozwoski

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