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Find the Boolean expression, in both sum-of-products (SOP) and product-of-sums (POS) forms, for the logic represented A 0 0 OOO 0 0 1 B 0 0 1 1 0 OHH 0 C 0 1 0 1 0 1 1 1 1 0 1 1 1 C Y OTO0 1 LOLO 0 0 the following truth table.

Find the Boolean expression, in both sum-of-products (SOP) and product-of-sums (POS) forms, for the logic represented A 0 0 OOO 0 0 1 B 0 0 1 1 0 OHH 0 C 0 1 0 1 0 1 1 1 1 0 1 1 1 C Y OTO0 1 LOLO 0 0 the following truth table.

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
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**Boolean Expression from Truth Table** **Objective:** 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. **Truth Table:** | A | B | C | Y | |---|---|---|---| | 0 | 0 | 0 | 1 | | 0 | 0 | 1 | 1 | | 0 | 1 | 0 | 0 | | 0 | 1 | 1 | 0 | | 1 | 0 | 0 | 1 | | 1 | 0 | 1 | 0 | | 1 | 1 | 0 | 1 | | 1 | 1 | 1 | 0 | **Analysis:** 1. **Sum-of-Products (SOP) Form:** - SOP form is obtained by OR-ing the AND terms corresponding to the rows where the output Y is 1. - The rows with Y = 1 are (A, B, C) = (0, 0, 0), (0, 0, 1), (1, 0, 0), and (1, 1, 0). - SOP Expression: Y = (A'B'C') + (A'B'C) + (AB'C') + (ABC') 2. **Product-of-Sums (POS) Form:** - POS form is obtained by AND-ing the OR terms corresponding to the rows where the output Y is 0. - The rows with Y = 0 are (A, B, C) = (0, 1, 0), (0, 1, 1), (1, 0, 1), and (1, 1, 1). - POS Expression: Y = (A + B' + C) (A + B + C') (A' + B + C') (A' + B' + C') Note: In these expressions, apostrophes (') denote NOT operation (negation), + denotes OR operation, and concatenation (AB) denotes AND operation.
Transcribed Image Text:**Boolean Expression from Truth Table** **Objective:** 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. **Truth Table:** | A | B | C | Y | |---|---|---|---| | 0 | 0 | 0 | 1 | | 0 | 0 | 1 | 1 | | 0 | 1 | 0 | 0 | | 0 | 1 | 1 | 0 | | 1 | 0 | 0 | 1 | | 1 | 0 | 1 | 0 | | 1 | 1 | 0 | 1 | | 1 | 1 | 1 | 0 | **Analysis:** 1. **Sum-of-Products (SOP) Form:** - SOP form is obtained by OR-ing the AND terms corresponding to the rows where the output Y is 1. - The rows with Y = 1 are (A, B, C) = (0, 0, 0), (0, 0, 1), (1, 0, 0), and (1, 1, 0). - SOP Expression: Y = (A'B'C') + (A'B'C) + (AB'C') + (ABC') 2. **Product-of-Sums (POS) Form:** - POS form is obtained by AND-ing the OR terms corresponding to the rows where the output Y is 0. - The rows with Y = 0 are (A, B, C) = (0, 1, 0), (0, 1, 1), (1, 0, 1), and (1, 1, 1). - POS Expression: Y = (A + B' + C) (A + B + C') (A' + B + C') (A' + B' + C') Note: In these expressions, apostrophes (') denote NOT operation (negation), + denotes OR operation, and concatenation (AB) denotes AND operation.
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