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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 COO 0 0 0 0 1 1 1 1 BOO 0 0 1 1 0 0 1 1 C 0 1 0 1 0 1 HOT 0 1 Y 0 |TLOOTO 1 1 0 0 1 1

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 COO 0 0 0 0 1 1 1 1 BOO 0 0 1 1 0 0 1 1 C 0 1 0 1 0 1 HOT 0 1 Y 0 |TLOOTO 1 1 0 0 1 1

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
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**Title:** Boolean Expression Derivation **Objective:** Find the Boolean expression in both sum-of-products (SOP) and product-of-sums (POS) forms, for the logic represented by the given truth table. **Truth Table:** ``` | A | B | C | Y | |---|---|---|---| | 0 | 0 | 0 | 0 | | 0 | 0 | 1 | 1 | | 0 | 1 | 0 | 1 | | 0 | 1 | 1 | 0 | | 1 | 0 | 0 | 1 | | 1 | 0 | 1 | 1 | | 1 | 1 | 0 | 1 | | 1 | 1 | 1 | 1 | ``` **Explanation:** - **Columns:** - **A, B, C:** Input variables. - **Y:** Output variable. - **Rows:** - The table lists all possible combinations of binary inputs (0s and 1s) and the corresponding output Y for each set of inputs. **Diagrams:** - No specific diagrams are present in this representation, as it is purely a tabular form. **Graph Explanation (Hypothetical):** - If there were a graph or diagram, it might visualize the truth table by mapping each input combination to the output using nodes for each state. **Next Steps (for Students):** 1. **SOP Form:** - Identify rows where Y = 1 and write the product (AND) of literals for each row. - Sum (OR) these products together. 2. **POS Form:** - Identify rows where Y = 0 and write the sum (OR) of literals for each row. - Product (AND) these sums together. Understanding how to interpret and convert truth tables into Boolean expressions is essential in digital logic design and computer engineering.
Transcribed Image Text:**Title:** Boolean Expression Derivation **Objective:** Find the Boolean expression in both sum-of-products (SOP) and product-of-sums (POS) forms, for the logic represented by the given truth table. **Truth Table:** ``` | A | B | C | Y | |---|---|---|---| | 0 | 0 | 0 | 0 | | 0 | 0 | 1 | 1 | | 0 | 1 | 0 | 1 | | 0 | 1 | 1 | 0 | | 1 | 0 | 0 | 1 | | 1 | 0 | 1 | 1 | | 1 | 1 | 0 | 1 | | 1 | 1 | 1 | 1 | ``` **Explanation:** - **Columns:** - **A, B, C:** Input variables. - **Y:** Output variable. - **Rows:** - The table lists all possible combinations of binary inputs (0s and 1s) and the corresponding output Y for each set of inputs. **Diagrams:** - No specific diagrams are present in this representation, as it is purely a tabular form. **Graph Explanation (Hypothetical):** - If there were a graph or diagram, it might visualize the truth table by mapping each input combination to the output using nodes for each state. **Next Steps (for Students):** 1. **SOP Form:** - Identify rows where Y = 1 and write the product (AND) of literals for each row. - Sum (OR) these products together. 2. **POS Form:** - Identify rows where Y = 0 and write the sum (OR) of literals for each row. - Product (AND) these sums together. Understanding how to interpret and convert truth tables into Boolean expressions is essential in digital logic design and computer engineering.
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