Homework Help is Here – Start Your Trial Now!
Engineering
Computer Science
Find the Boolean expression, in both sum-of-products (SOP) and product-of-sums (POS) forms, for the logic represented by the following truth table. A оооонннн B оонноонн C нонононо Y 1 177 1 0 ооо

Find the Boolean expression, in both sum-of-products (SOP) and product-of-sums (POS) forms, for the logic represented by the following truth table. A оооонннн B оонноонн C нонононо Y 1 177 1 0 ооо

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
See similar textbooks
icon
Related questions
Question
### Boolean Expression from Truth Table Given the task of finding the Boolean expression in both sum-of-products (SOP) and product-of-sums (POS) forms, analyze the provided truth table to understand the logic: #### Truth Table | A | B | C | Y | |---|---|---|---| | 0 | 0 | 0 | 1 | | 0 | 0 | 1 | 1 | | 0 | 1 | 0 | 1 | | 0 | 1 | 1 | 1 | | 1 | 0 | 0 | 0 | | 1 | 0 | 1 | 0 | | 1 | 1 | 0 | 0 | | 1 | 1 | 1 | 0 | #### Explanation of the Table - **Columns:** The first three columns represent inputs A, B, and C. The fourth column, Y, represents the output. - **Rows:** Each row shows a unique combination of inputs and the resulting output. ### Sum-of-Products (SOP) Expression The SOP expression considers the rows where the output Y is 1 (logical high). **For this table:** - Rows 0, 1, 2, and 3 have Y = 1. **SOP Equation:** - \( Y = \overline{A} \overline{B} \overline{C} + \overline{A} \overline{B} C + \overline{A} B \overline{C} + \overline{A} B C \) ### Product-of-Sums (POS) Expression The POS expression is derived by considering rows where the output Y is 0 (logical low). **For this table:** - Rows 4, 5, 6, and 7 have Y = 0. **POS Equation:** - \( Y = (A + B + C)(A + B + \overline{C})(A + \overline{B} + C)(A + \overline{B} + \overline{C}) \) These logical expressions are crucial for simplifying complex logic circuits and are used in various digital systems.
Transcribed Image Text:### Boolean Expression from Truth Table Given the task of finding the Boolean expression in both sum-of-products (SOP) and product-of-sums (POS) forms, analyze the provided truth table to understand the logic: #### Truth Table | A | B | C | Y | |---|---|---|---| | 0 | 0 | 0 | 1 | | 0 | 0 | 1 | 1 | | 0 | 1 | 0 | 1 | | 0 | 1 | 1 | 1 | | 1 | 0 | 0 | 0 | | 1 | 0 | 1 | 0 | | 1 | 1 | 0 | 0 | | 1 | 1 | 1 | 0 | #### Explanation of the Table - **Columns:** The first three columns represent inputs A, B, and C. The fourth column, Y, represents the output. - **Rows:** Each row shows a unique combination of inputs and the resulting output. ### Sum-of-Products (SOP) Expression The SOP expression considers the rows where the output Y is 1 (logical high). **For this table:** - Rows 0, 1, 2, and 3 have Y = 1. **SOP Equation:** - \( Y = \overline{A} \overline{B} \overline{C} + \overline{A} \overline{B} C + \overline{A} B \overline{C} + \overline{A} B C \) ### Product-of-Sums (POS) Expression The POS expression is derived by considering rows where the output Y is 0 (logical low). **For this table:** - Rows 4, 5, 6, and 7 have Y = 0. **POS Equation:** - \( Y = (A + B + C)(A + B + \overline{C})(A + \overline{B} + C)(A + \overline{B} + \overline{C}) \) These logical expressions are crucial for simplifying complex logic circuits and are used in various digital systems.
Expert Solution
steps

Step by step

Solved in 3 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Embedded software development
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, computer-science and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Database System Concepts
Database System Concepts
Computer Science
ISBN:
9780078022159
Author:
Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:
McGraw-Hill Education
Starting Out with Python (4th Edition)
Starting Out with Python (4th Edition)
Computer Science
ISBN:
9780134444321
Author:
Tony Gaddis
Publisher:
PEARSON
Digital Fundamentals (11th Edition)
Digital Fundamentals (11th Edition)
Computer Science
ISBN:
9780132737968
Author:
Thomas L. Floyd
Publisher:
PEARSON
C How to Program (8th Edition)
C How to Program (8th Edition)
Computer Science
ISBN:
9780133976892
Author:
Paul J. Deitel, Harvey Deitel
Publisher:
PEARSON
Database Systems: Design, Implementation, & Manag…
Database Systems: Design, Implementation, & Manag…
Computer Science
ISBN:
9781337627900
Author:
Carlos Coronel, Steven Morris
Publisher:
Cengage Learning
Programmable Logic Controllers
Programmable Logic Controllers
Computer Science
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education
SEE MORE TEXTBOOKS