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Use the rules of Boolean algebra to find the maximum SOP simplification of the function represented by the following truth tabl A 0 0 0 0 1 1 1 1 B 0 0 1 1 0 0 1 1 C 0 1 0 1 0 1 0 1 Y 1 0 1 0 0 1

Use the rules of Boolean algebra to find the maximum SOP simplification of the function represented by the following truth tabl A 0 0 0 0 1 1 1 1 B 0 0 1 1 0 0 1 1 C 0 1 0 1 0 1 0 1 Y 1 0 1 0 0 1

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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**Title: Boolean Algebra: Simplifying Functions Using SOP** **Introduction:** In this lesson, we will explore how to use Boolean algebra to find the Sum of Products (SOP) simplification of a function using a truth table. A truth table is a mathematical table used in logic—specifically in connection with Boolean algebra, Boolean functions, and propositional calculus—which sets out the functional values of logical expressions based on their arguments. **Truth Table Analysis:** Below is the truth table representing the logical function. | A | B | C | Y | |---|---|---|---| | 0 | 0 | 0 | 1 | | 0 | 0 | 1 | 0 | | 0 | 1 | 0 | 1 | | 0 | 1 | 1 | 0 | | 1 | 0 | 0 | 0 | | 1 | 0 | 1 | 0 | | 1 | 1 | 0 | 1 | | 1 | 1 | 1 | 0 | **Explanation of the Table:** - Column A, B, and C represent the inputs, each capable of being either 0 (False) or 1 (True). - Column Y is the output of the function for every combination of A, B, and C. - The table shows the result of the function for each particular input combination, totaling 8 possible states (since there are three inputs, yielding \(2^3 = 8\) combinations). **Objective:** The goal is to express the Boolean function Y in its maximum SOP form using the indicated outputs from the truth table. **Steps to Derive SOP Expression:** 1. **Identify Rows Where Y = 1**: - These are the rows that contribute to the SOP expression. - From the table, these rows are: (0, 0, 0), (0, 1, 0), and (1, 1, 0). 2. **Write Product Terms for Each Row**: - For (0, 0, 0), the term is \(\overline{A}\overline{B}\overline{C}\) - For (0, 1, 0), the term is \(\overline{A}B\overline{C}\) - For (1
Transcribed Image Text:**Title: Boolean Algebra: Simplifying Functions Using SOP** **Introduction:** In this lesson, we will explore how to use Boolean algebra to find the Sum of Products (SOP) simplification of a function using a truth table. A truth table is a mathematical table used in logic—specifically in connection with Boolean algebra, Boolean functions, and propositional calculus—which sets out the functional values of logical expressions based on their arguments. **Truth Table Analysis:** Below is the truth table representing the logical function. | A | B | C | Y | |---|---|---|---| | 0 | 0 | 0 | 1 | | 0 | 0 | 1 | 0 | | 0 | 1 | 0 | 1 | | 0 | 1 | 1 | 0 | | 1 | 0 | 0 | 0 | | 1 | 0 | 1 | 0 | | 1 | 1 | 0 | 1 | | 1 | 1 | 1 | 0 | **Explanation of the Table:** - Column A, B, and C represent the inputs, each capable of being either 0 (False) or 1 (True). - Column Y is the output of the function for every combination of A, B, and C. - The table shows the result of the function for each particular input combination, totaling 8 possible states (since there are three inputs, yielding \(2^3 = 8\) combinations). **Objective:** The goal is to express the Boolean function Y in its maximum SOP form using the indicated outputs from the truth table. **Steps to Derive SOP Expression:** 1. **Identify Rows Where Y = 1**: - These are the rows that contribute to the SOP expression. - From the table, these rows are: (0, 0, 0), (0, 1, 0), and (1, 1, 0). 2. **Write Product Terms for Each Row**: - For (0, 0, 0), the term is \(\overline{A}\overline{B}\overline{C}\) - For (0, 1, 0), the term is \(\overline{A}B\overline{C}\) - For (1
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