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Electronic Labs_101

Electronic Labs_101 - Boolean Laws and DeMorgan’s Theorem...

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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 2-input AND gate One LED Four-position DIP switch Four l-kfl resistors Three 0.1-uF 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 0.1-uF capacitor between VCC and ground for each IC 67 ...
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