**Problem #06**: Using the truth table below, develop a simplified SOP expression using a Karnaugh Map.| Inputs | Output ||--------|--------|| A B C | X || 0 0 0 | 1 || 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 |To solve this problem, you will use the given truth table and represent it on a Karnaugh Map in order to find the simplified Sum of Products (SOP) expression. Each row of the truth table represents a minterm where the output \( X \) is equal to 1.

Answered: Problem_#06] Using the truth table…

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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**Problem #06**: Using the truth table below, develop a simplified SOP expression using a Karnaugh Map.

| Inputs | Output |
|--------|--------|
| A B C | X |
| 0 0 0 | 1 |
| 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 |

To solve this problem, you will use the given truth table and represent it on a Karnaugh Map in order to find the simplified Sum of Products (SOP) expression. Each row of the truth table represents a minterm where the output \( X \) is equal to 1.

Expert Solution

Step 1: Providing Introduction

K-Map:

An alternative to using difficult theorems or manipulating equations is to utilize a visual tool called a Karnaugh map (K-map) to simplify the algebraic expressions of Boolean functions.

SOP expression :

The Sum of Product (SOP) expression results from adding the sum of two or more products (AND) (OR). In other words, the final AND-OR logical output is created by essentially ORing the outputs of two or more AND gates with the input of an OR gate.

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