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3. For the following truth table, a 0 0 0 0 1 1 1 1 b POOLLOO 0 0 1 1 0 0 1 1 cf 0 1 COLO 0 1 0 1 0 0 1 1 1 0 0 1 1 1 1) Show the sum of minterms in numerical form. 2) Show an algebraic expression in sum of minterms form and draw the logic diagram. 3) Simplify the sum of minterms form to a minimum SOP expression (three terms, six literals). Show each step of the simplification. Draw the logic diagram using the minimum SOP expression.

3. For the following truth table, a 0 0 0 0 1 1 1 1 b POOLLOO 0 0 1 1 0 0 1 1 cf 0 1 COLO 0 1 0 1 0 0 1 1 1 0 0 1 1 1 1) Show the sum of minterms in numerical form. 2) Show an algebraic expression in sum of minterms form and draw the logic diagram. 3) Simplify the sum of minterms form to a minimum SOP expression (three terms, six literals). Show each step of the simplification. Draw the logic diagram using the minimum SOP expression.

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 Boolean Algebra Problem Set** Consider the following truth table: | a | b | c | f | |---|---|---|---| | 0 | 0 | 0 | 0 | | 0 | 0 | 1 | 1 | | 0 | 1 | 0 | 0 | | 0 | 1 | 1 | 1 | | 1 | 0 | 0 | 1 | | 1 | 0 | 1 | 0 | | 1 | 1 | 0 | 1 | | 1 | 1 | 1 | 1 | **Tasks:** 1) **Sum of Minterms in Numerical Form:** - Identify and list the minterms where the function \( f \) equals 1. 2) **Algebraic Expression Using Sum of Minterms and Logic Diagram:** - Express \( f \) as a sum of minterms. - Draw the logic diagram corresponding to this expression. 3) **Simplification to Minimum SOP Expression:** - Simplify the sum of minterms to obtain a minimum SOP (Sum of Products) expression with three terms and six literals. - Show each simplification step. - Illustrate the logic diagram using the simplified SOP expression. 4) **Product of Maxterms in Numerical Form:** - Identify and write down the maxterms corresponding to the function \( f \). 5) **Algebraic Expression Using Product of Maxterms:** - Express \( f \) as a product of maxterms. 6) **Simplification to Minimum POS Expression:** - Simplify the product of maxterms to achieve a minimum POS (Product of Sums) expression featuring two terms and five literals. - Detail each step of the simplification process. For each task, carefully consider the transformation steps and ensure logical consistency throughout the problem-solving process for optimal learning outcomes.
Transcribed Image Text:**Truth Table and Boolean Algebra Problem Set** Consider the following truth table: | a | b | c | f | |---|---|---|---| | 0 | 0 | 0 | 0 | | 0 | 0 | 1 | 1 | | 0 | 1 | 0 | 0 | | 0 | 1 | 1 | 1 | | 1 | 0 | 0 | 1 | | 1 | 0 | 1 | 0 | | 1 | 1 | 0 | 1 | | 1 | 1 | 1 | 1 | **Tasks:** 1) **Sum of Minterms in Numerical Form:** - Identify and list the minterms where the function \( f \) equals 1. 2) **Algebraic Expression Using Sum of Minterms and Logic Diagram:** - Express \( f \) as a sum of minterms. - Draw the logic diagram corresponding to this expression. 3) **Simplification to Minimum SOP Expression:** - Simplify the sum of minterms to obtain a minimum SOP (Sum of Products) expression with three terms and six literals. - Show each simplification step. - Illustrate the logic diagram using the simplified SOP expression. 4) **Product of Maxterms in Numerical Form:** - Identify and write down the maxterms corresponding to the function \( f \). 5) **Algebraic Expression Using Product of Maxterms:** - Express \( f \) as a product of maxterms. 6) **Simplification to Minimum POS Expression:** - Simplify the product of maxterms to achieve a minimum POS (Product of Sums) expression featuring two terms and five literals. - Detail each step of the simplification process. For each task, carefully consider the transformation steps and ensure logical consistency throughout the problem-solving process for optimal learning outcomes.
Expert Solution
Step 1: Boolean expression

As per guidelines, i'm supposed to answer first 3 sub parts.


Introduction

Any Boolean function can be expressed as a sum (OR) of its 1- Min terms.

Any Boolean function can be expressed as a product (AND) of its 0 - Max terms.


Given truth table


a

b

c

F

0

0

0

0

0

1

0

0

1

1

2

0

1

0

0

3

0

1

1

1

4

1

0

0

1

5

1

0

1

0

6

1

1

0

1

7

1

1

1

1


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