Lab 4 Combinational Logic Circuits

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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 4: Combinational Logic Circuits Laboratory Report for EENG 3302. 001 College of Engineering and Computer Science Department of Electrical Engineering University of Texas at Tyler Tyler, TX 10/04/2023 Annika McNeal A BSTRACT The goal of this experiment is to compare combinational logic circuits before and after simplifying them using basic laws, Boolean algebra and De Morgan’s theorem.
Lab 4: Combinational Logic Circuits Annika McNeal I. P ROJECT DESCRIPTION The purpose of this experiment is to take complex expressions and convert them to their simplest form using Boolean algebra, De Morgan’s theorem, basic laws and Karnaugh maps. Once in its simplest form, apply the new expression to create combinational logic circuits on Multisim. II. T HEORETICAL BACKGROUND De Morgan’s Theorem’s ¿ Boolean Algebra 1) A + 0 = A 7) A * A = A 2) A + 1 = 1 8) A * ´ A = 0 3) A * 0 = 0 9) ´ A = A 4) A * 1 = A 10) A + AB = A 5) A + A = 1 11) A + ´ A B = A + B 6) A + ´ A = 1 12) (A + B)(A + C) = A + BC III. M ETHODS AND MATERIALS Minimal materials are needed to perform the experiment. After algebra and theorems are applied, Multisim is utilized to create the combinational circuit before and after simplification. Equipment Instrument Function/Description Multisim Software application which is utilized to simulate an electronic circuit board 1
Lab 4: Combinational Logic Circuits Annika McNeal Experimental procedure Example 4: Using basic laws, Boolean algebra, and De Morgan’s theorem simplify the expression and use the Karnaugh map to verify the SOP form. A ´ BC + ´ A BC + ´ A ´ BC + A Circuit 4 un-simplified: Simplification: 2
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Lab 4: Combinational Logic Circuits Annika McNeal Problem 1: Follow the same procedure as example 4. A ´ B + ´ A ( B + C ) + B ´ B + C Un-simplified Circuit 1 Boolean and De Morgan’s algebra: A ´ B + ´ A ( B + C ) + B ´ B + C = A ´ B + ´ A + ´ B + C + B ´ B + C = A ´ B + ´ A + ´ B ´ C + B* ´ B ´ C = ´ B + ´ A + ´ B ´ C = ´ B + ´ A Next modify the expression into SOP form to use it into a Karnaugh map. Karnaugh Map: SOP form: ´ A ´ B ´ C + ´ A ´ BC + ´ A B ´ C + ´ A BC + A ´ B ´ C + A ´ BC 3
Lab 4: Combinational Logic Circuits Annika McNeal Problem 2 : Repeat the procedure from example 4. AB ´ C + ´ A ´ BC + ´ A BC + ´ A ´ B ´ C Un-simplified circuit 2 Boolean Algebra: = AB ´ C + ´ A C ( ´ B + B ) + ´ A ´ B ´ C = AB ´ C + ´ A C + ´ A ´ B ´ C = AB ´ C + ´ A (C + ´ B ´ C ) = AB ´ C + ´ A (C + ´ B ) = AB ´ C + ´ A ´ B + ´ A ´ C 4
Lab 4: Combinational Logic Circuits Annika McNeal Problem 3: Repeat steps from problem 1. ´ AB + ´ AC + ´ A ´ B ´ C Un-simplified circuit 3 Basic, Boolean, and De Morgan’s algebra: = ´ A + ´ B + ´ A + ´ C + ´ A ´ B ´ C = ´ A + ´ B + ´ C + ´ A ´ B ´ C = ´ A + ´ B + ´ C SOP form: IV. R ESULTS 5
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Lab 4: Combinational Logic Circuits Annika McNeal C IRCUIT 4 R ESULTS : Circuit 4 simplified Circuit 4: Truth Table Inputs Un-simplified Outputs Simplifie d Output s A B C A B + AC ´ ¿¿ + ´ A BC ´ B + ´ AC 0 0 0 1 1 0 0 1 1 1 0 1 0 0 0 0 1 1 1 1 1 0 0 1 1 1 0 1 1 1 1 1 0 0 0 1 1 1 0 0 Karnaugh map: 6
Lab 4: Combinational Logic Circuits Annika McNeal C IRCUIT 1 R ESULTS : S IMPLIFIED C IRCUIT 1 Circuit 1: Truth Table Inputs Un-simplified Outputs Simplifie d Output s A B C A ´ B + ¿ A ´ ( B + C )+ ¿ B ´ ( B + C ) A ´ B 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 1 1 0 0 1 0 0 1 1 1 0 1 1 1 1 1 0 0 0 7
Lab 4: Combinational Logic Circuits Annika McNeal 1 1 1 0 0 Karnaugh map: CIRCUIT 2: Results Simplified circuit 2 Circuit 2 truth table: Inputs Un-simplified Outputs Simplified Outputs A B C AB ´ C + ´ A ´ BC + ´ A BC + ´ A ´ B ´ C AB ´ C + ´ A ´ B + ´ A ´ C 0 0 0 1 1 0 0 1 1 1 0 1 0 0 0 0 1 1 1 1 1 0 0 0 0 1 0 1 0 0 1 1 0 1 1 1 1 1 0 0 8
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Lab 4: Combinational Logic Circuits Annika McNeal Karnaugh Map: CIRCUIT 3 :Results Simplified Circuit 3 Circuit 3 Truth Table: Inputs Un-simplified Outputs Simplifie d Output s A B C A ´ B + ¿ A ´ ( B + C )+ ¿ B ´ ( B + C ) A ´ B 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 1 1 0 0 9
Lab 4: Combinational Logic Circuits Annika McNeal 1 0 0 1 1 1 0 1 1 1 1 1 0 0 0 1 1 1 0 0 Karnaugh map: V. D ISCUSSION De Morgan’s theorems and the basic laws prove very useful for simplifying Boolean logic expressions because of the way they can break an inversion, which could be the complement of a complex Boolean expression. Reducing the number of gates in a circuit, whilst keeping its functionality, allows for less time in the design process can be cost and time efficient. VI. C ONCLUSIONS Based on the results a conclusion can be drawn that simplifying the expression prior to creating the logic will create a less complex circuit that produces the same outcomes. 10

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