Lab 3 De Morgans Theorem

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University of Texas, Tyler *

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3302

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Electrical Engineering

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Oct 30, 2023

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Lab 3: De Morgans Theorem Laboratory Report for EENG 3302 College of Engineering and Computer Science Department of Electrical Engineering University of Texas at Tyler Tyler, TX 9/26/2023 Annika McNeal A BSTRACT The focus of this lab is to implement AND, OR, NOT, and NAND gates into a given circuit and be able to successfully apply De Morgans theorems to simplify Booleans expressions.

Lab 3: De Morgans Theorem Annika McNeal I. P ROJECT DESCRIPTION In this experiment we build compare circuits by constructing them with Boolean algebra and the same circuit with De Morgans theorem applied. II. T HEORETICAL BACKGROUND De Morgans first theorem: The complement of two or more ANDed variables is equivalent to the OR of the complements of the variables. De Morgans second theorem: The complement of two or more ORed variables is equivalent to the AND of the complements of the individual variables. III. M ETHODS AND MATERIALS Equipment Instrument Function/Description Breadboard Allows for solderless circuit construction Multisim Software application which is utilized to simulate an electronic circuit board 7400 Logic gate Two-input NAND gate 7404 Logic gate NOT inverter gate 7408 Logic gate Two-input AND gate 7432 Logic gate Two-input OR gate Experimental procedure  For the first procedure, inputs A, B, and C are connected to gates AND, OR, and NOT on the breadboard to replicate the diagram from the report. Figure 1 proved De Morgans first theorem by demonstrating that two or more ANDed variables is equivalent to the OR of the complements of the variables by producing the same HIGH and LOW outputs given on the truth table. The expression below proves correct. ´ ( AB + C ) ( A + BC ) = ( ´ A + ´ B ) ´ C + ´ A ( ´ B + ´ C ) 77414c5b696f12097bd004336b7b755b3445c118.docx 1

Lab 3: De Morgans Theorem Annika McNeal Circuit 1  For the second procedure Multisim is utilized to create a circuit diagram with De Morgan’s applied to the expression. The output is displayed using a digital probe indicator (PROBE_DIG_GREEN), that illuminates ON and OFF to represent HIGH and LOW outputs. With the results a truth table can be created and determine if the theorem is correct. ´ ( A + B + C ) D = ´ A ∗ ´ B ∗ ´ C + ´ D  The third expression follows the same procedure as the second one. ´ A + B + ¿ ´ C ´ ¿ = (A+B)C Our first step was to construct a circuit as 77414c5b696f12097bd004336b7b755b3445c118.docx 2

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Lab 3: De Morgans Theorem Annika McNeal seen in (figure 2) using the OR gate and record the output from the circuit with one input going through the pulse generator and the other input connected to ground. We would measure with the output of the timing diagram with the oscilloscope. (Table 2) 77414c5b696f12097bd004336b7b755b3445c118.docx 3

Lab 3: De Morgans Theorem Annika McNeal We then did the same thing as in the first step but we recorded both inputs. (Table 2) For the third step in our lab, we changed from the OR gate to the AND gate and recorded both input as the same in our second step and measured the output of the timing diagram with the oscilloscop 77414c5b696f12097bd004336b7b755b3445c118.docx 4

Lab 3: De Morgans Theorem Annika McNeal Our first step was to construct a circuit as seen in (figure 2) using the OR gate and record the output from the circuit with one input going through the pulse generator and the other input connected to ground. We would measure with the 77414c5b696f12097bd004336b7b755b3445c118.docx 5

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Lab 3: De Morgans Theorem Annika McNeal output of the timing diagram with the oscilloscope. (Table 2) We then did the same thing as in the first step but we recorded both inputs. (Table 2) For the third step in our lab, we changed from the OR gate to the AND gate and recorded both input as the same in our second step and measured the output of the timing 77414c5b696f12097bd004336b7b755b3445c118.docx 6

Lab 3: De Morgans Theorem Annika McNeal diagram with the oscilloscop IV. R ESULTS Circuit 1 Circuit 2 77414c5b696f12097bd004336b7b755b3445c118.docx 7

Lab 3: De Morgans Theorem Annika McNeal Circuit 2: Truth Table Circuit 3 Circuit 3: Truth Table Inputs Outputs 77414c5b696f12097bd004336b7b755b3445c118.docx 8 Inputs Outputs A (U13) B (U 14) C (U15) (A + B) C 0 0 0 1 0 0 1 0 0 1 1 1 0 1 0 1 1 0 0 1 1 1 0 1 1 1 1 1 1 0 1 1

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Lab 3: De Morgans Theorem Annika McNeal A (U4) B (U5) C (U6) D (U7) ´ A ´ B ´ C + ´ D (X1) 0 0 0 0 1 0 0 0 1 1 0 0 1 1 0 0 1 1 1 0 0 1 0 1 0 1 1 1 0 1 1 1 0 0 1 1 0 0 0 1 1 0 1 0 1 V. D ISCUSSION To apply De Morgan’s theorem to the expression, break the overbar covering both terms and change the sign between the terms. This results in changing the complements to the literal variables and switching the gates between OR or AND operations. Both theorems can be applied interchangeable to what fits the expression best. VI. C ONCLUSIONS In conclusion, we can determine that De Morgan’s theorems are true and can be applied to any Boolean Algebra expression. Using his theorems made the process of creating circuits with the breadboard and Multisim simpler and more efficient. 77414c5b696f12097bd004336b7b755b3445c118.docx 9