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7. Given the following truth table, write an algebraic expression for the given function and simplify the expression using a Karnaugh map. А В F 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

7. Given the following truth table, write an algebraic expression for the given function and simplify the expression using a Karnaugh map. А В F 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 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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### Truth Table and Karnaugh Map for Boolean Algebra #### Problem Statement: Given the following truth table, write an algebraic expression for the given function and simplify the expression using a Karnaugh map. #### Truth Table: | A | B | C | F | |---|---|---|---| | 0 | 0 | 0 | 1 | | 0 | 0 | 1 | 1 | | 0 | 1 | 0 | 1 | | 0 | 1 | 1 | 0 | | 1 | 0 | 0 | 0 | | 1 | 0 | 1 | 1 | | 1 | 1 | 0 | 0 | | 1 | 1 | 1 | 1 | - **Columns:** - A, B, C: Input variables. - F: Output value for each combination of inputs. #### Instructions: 1. **Write an Algebraic Expression:** Identify the rows where the output F is 1, and write the corresponding min terms (product of inputs) for each. 2. **Karnaugh Map Simplification:** Use a Karnaugh map to simplify the obtained expression by grouping adjacent ones and deriving a simplified algebraic expression.
Transcribed Image Text:### Truth Table and Karnaugh Map for Boolean Algebra #### Problem Statement: Given the following truth table, write an algebraic expression for the given function and simplify the expression using a Karnaugh map. #### Truth Table: | A | B | C | F | |---|---|---|---| | 0 | 0 | 0 | 1 | | 0 | 0 | 1 | 1 | | 0 | 1 | 0 | 1 | | 0 | 1 | 1 | 0 | | 1 | 0 | 0 | 0 | | 1 | 0 | 1 | 1 | | 1 | 1 | 0 | 0 | | 1 | 1 | 1 | 1 | - **Columns:** - A, B, C: Input variables. - F: Output value for each combination of inputs. #### Instructions: 1. **Write an Algebraic Expression:** Identify the rows where the output F is 1, and write the corresponding min terms (product of inputs) for each. 2. **Karnaugh Map Simplification:** Use a Karnaugh map to simplify the obtained expression by grouping adjacent ones and deriving a simplified algebraic expression.
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