AB 00 01 11 10 00 0 1 1 。 01 1 1 1 1 CD 11 1 1 1 。 10 D 1 1 。
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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Question
Derive the simplest Boolean function possible that implements the given Kmap (see image).
Transcribed Image Text:The table shown is a Karnaugh map (K-map), which is used for simplifying boolean algebra expressions. It is structured to represent a four-variable function across inputs labeled as AB and CD.
### Transcription:
**Header**: CD
**Rows and Columns**: Each cell corresponds to a specific combination of inputs for the variables AB and CD. The values are:
- **AB rows**:
- **00**: 0, 1, 1, 0
- **01**: 1, 1, 1, 1
- **11**: 1, 1, 1, 1
- **10**: 0, 1, 0, 0
**Explanation:**
- **AB Labels**:
- Horizontal labels represent every possible binary combination of variables A and B: 00, 01, 11, 10.
- **CD Labels**:
- Vertical labels represent every possible binary combination of variables C and D: 00, 01, 11, 10.
- **Cell Values**:
- Each cell contains a binary value (0 or 1), which corresponds to the function's output for the respective combination of inputs.
This K-map can be used for logic minimization in digital circuit design to create simplified expressions.
Expert Solution
Step 1
| C.D | C.D | C.D | C.D | |
| A.B | 0 | 1 | 1 | 0 |
| A.B | 1 | 1 | 1 | 1 |
| A.B | 1 | 1 | 1 | 1 |
| A.B | 0 | 1 | 0 | 0 |
| C.D | C.D | C.D | C.D | |
| A.B | 0 | 1 | 3 | 2 |
| A.B | 4 | 5 | 7 | 6 |
| A.B | 12 | 13 | 15 | 14 |
| A.B | 8 | 9 | 11 | 10 |
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