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
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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.
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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