13. Give the Boolean expression for the following circuit diagram. A
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 13: Boolean Expression for the Circuit Diagram
Below is the description and analysis of the provided circuit diagram to obtain the Boolean expression.
#### Components and Connections:
1. **Inputs**: A, B, C
2. **Gates**:
- **NOT Gate**: Inverts input A.
- **AND Gate 1**: Takes inputs B and inverted A (output of NOT Gate).
- **NOT Gate**: Inverts input C.
- **AND Gate 2**: Takes inputs C and B.
- **OR Gate**: Combines outputs from AND Gate 1 and AND Gate 2.
#### Detailed Analysis:
- **NOT Gate** takes input A and outputs NOT A (¬A).
- **AND Gate 1** processes inputs B and output of the NOT Gate (¬A), resulting in the expression: B · ¬A.
- **AND Gate 2** processes inputs B and C, resulting in the expression: B · C.
- **OR Gate** takes the results from both AND gates:
- Output of AND Gate 1: B · ¬A
- Output of AND Gate 2: B · C
The OR Gate output is the sum of these products: (B · ¬A) + (B · C)
### Resulting Boolean Expression
The Boolean expression representing the logic of the circuit is:
\[ (B \cdot \neg A) + (B \cdot C) \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F29d14185-3740-4cf8-89ba-8a2b3461623a%2Fd162c966-f2a0-4dce-97a1-6369153c83db%2Fa72rakd_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem 13: Boolean Expression for the Circuit Diagram
Below is the description and analysis of the provided circuit diagram to obtain the Boolean expression.
#### Components and Connections:
1. **Inputs**: A, B, C
2. **Gates**:
- **NOT Gate**: Inverts input A.
- **AND Gate 1**: Takes inputs B and inverted A (output of NOT Gate).
- **NOT Gate**: Inverts input C.
- **AND Gate 2**: Takes inputs C and B.
- **OR Gate**: Combines outputs from AND Gate 1 and AND Gate 2.
#### Detailed Analysis:
- **NOT Gate** takes input A and outputs NOT A (¬A).
- **AND Gate 1** processes inputs B and output of the NOT Gate (¬A), resulting in the expression: B · ¬A.
- **AND Gate 2** processes inputs B and C, resulting in the expression: B · C.
- **OR Gate** takes the results from both AND gates:
- Output of AND Gate 1: B · ¬A
- Output of AND Gate 2: B · C
The OR Gate output is the sum of these products: (B · ¬A) + (B · C)
### Resulting Boolean Expression
The Boolean expression representing the logic of the circuit is:
\[ (B \cdot \neg A) + (B \cdot C) \]
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