Unformatted text preview: Boolean Laws and DeMorgan’s Theorem Objectives After completing this experiment, you will be able to U Experimentally verify several of the rules for
Boolean algebra. D Design circuits to prove Rules 10 and 11. El Experimentally determine the truth tables for
circuits with three input variables, and use De
Morgan’s theorem to prove algebraically
whether they are equivalent. Reference Reading Floyd, Digital Fundamentals, 6th ed., Chapter 4, “Boolean Algebra and Logic Simpliﬁcation,” Sec
tions 4—~1 through 4—5. Materials Needed 4071 quad 2—input OR gate
4069 hex inverter 4081 quad 2input AND gate
One LED Fourposition DIP switch
Four lkﬂ resistors Three 0.1uF capacitors Summary of Theory Boolean algebra consists of a set of laws that govern
logical relationships. Unlike ordinary algebra, where an unknown can take any value, the elements of
Boolean algebra are binary variables and can have
only one of two values: 1 or 0. Symbols used in Boolean algebra include the
overbar, which is the NOT or complement; the con
nective + , which implies logical addition and is read
“OR”; and the connective , which implies logical mul
tiplication and is read “AND.” The dot is frequently
eliminated when logical multiplication is shown. Thus
A  B is writtenAB. The basic rules of Boolean algebra
are listed in Table 6—1 for convenience. The Boolean rules shown in Table 6—1 can be
applied to actual circuits, as this experiment demon
strates. For example, Rule 1 states A + O = A (re
member to read + as “OR”). This rule can be demon
strated with an OR gate and a pulse generator, as
shown in Figure 6—1. The signal from the pulse
generator is labeledA and the ground signal represents
the O. The output, which is a replica of the pulse
generator, represents the ORing of the two inputs—
hence, the rule is proved. Figure 6—1 illustrates this
rule. The circuits constructed in this experiment use
CMOS logic. You should use static protection as
outlined in the text and Experiment 5 to prevent
damage to your ICs. Procedure 1. Construct the circuit shown in Figure 6—1.
Set the power supply to +5.0 V and use a 0.1uF
capacitor between VCC and ground for each IC 67 ...
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 Fall '05
 Myer,B

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