Problem #07] Use a Karnaugh Map to derive the simplified SOP expression for the truth table shown below.
Problem #07] Use a Karnaugh Map to derive the simplified SOP expression for the truth table shown below.
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 #07**: Use a Karnaugh Map to derive the simplified SOP expression for the truth table shown below.
| Inputs | Output |
|--------|--------|
| A B C D| X |
| 0 0 0 0| 0 |
| 0 0 0 1| 1 |
| 0 0 1 0| 1 |
| 0 0 1 1| 0 |
| 0 1 0 0| 1 |
| 0 1 0 1| 1 |
| 0 1 1 0| 1 |
| 0 1 1 1| 0 |
| 1 0 0 0| 0 |
| 1 0 0 1| 1 |
| 1 0 1 0| 1 |
| 1 0 1 1| 0 |
| 1 1 0 0| 1 |
| 1 1 0 1| 1 |
| 1 1 1 0| 1 |
| 1 1 1 1| 1 |
**Explanation:**
The table presented includes four input variables labeled A, B, C, and D and an output variable labeled X. Each row of the table represents a possible combination of input values, with '1' indicating true and '0' indicating false. The output shows the result for each combination.
To simplify this using a Karnaugh Map, plot these inputs against their outputs, and look for groupings of 1s to minimize the Boolean expression in Sum of Products (SOP) form.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fee344c66-7efa-4594-9121-d91385396bb3%2Fa39a776a-d37b-4665-8c02-c1647c7a0341%2F3dsy6bo_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem #07**: Use a Karnaugh Map to derive the simplified SOP expression for the truth table shown below.
| Inputs | Output |
|--------|--------|
| A B C D| X |
| 0 0 0 0| 0 |
| 0 0 0 1| 1 |
| 0 0 1 0| 1 |
| 0 0 1 1| 0 |
| 0 1 0 0| 1 |
| 0 1 0 1| 1 |
| 0 1 1 0| 1 |
| 0 1 1 1| 0 |
| 1 0 0 0| 0 |
| 1 0 0 1| 1 |
| 1 0 1 0| 1 |
| 1 0 1 1| 0 |
| 1 1 0 0| 1 |
| 1 1 0 1| 1 |
| 1 1 1 0| 1 |
| 1 1 1 1| 1 |
**Explanation:**
The table presented includes four input variables labeled A, B, C, and D and an output variable labeled X. Each row of the table represents a possible combination of input values, with '1' indicating true and '0' indicating false. The output shows the result for each combination.
To simplify this using a Karnaugh Map, plot these inputs against their outputs, and look for groupings of 1s to minimize the Boolean expression in Sum of Products (SOP) form.
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