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

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

Database System Concepts
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
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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: \[ (B \cdot \neg A) + (B \cdot C) \]
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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