### Problem 13: Boolean Expression for the Circuit DiagramBelow is the description and analysis of the provided circuit diagram to obtain the Boolean expression.#### Components and Connections:1. **Inputs**: A, B, C2. **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 ExpressionThe Boolean expression representing the logic of the circuit is:\[ (B \cdot \neg A) + (B \cdot C) \]

13. Given circuit At 1 we get AB as it is AND gate At 2 we get B+C as it…

Answered: 13. Give the Boolean expression for the…

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13. Give the Boolean expression for the following circuit diagram. A

Database System Concepts

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Question

### 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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