Draw the truth table for a NAND gate.
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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1. Draw the truth table for a NAND gate.
![**Question 13: Give the Boolean expression for the following circuit diagram.**
**Circuit Diagram Explanation:**
The circuit diagram contains the following logic gates:
1. **NOT Gate:**
- Input: A
- Output: \( \overline{A} \)
2. **OR Gate:**
- Inputs: B and C
- Output: \( B + C \)
3. **AND Gate:**
- Inputs: Output of NOT Gate \( (\overline{A}) \) and B
- Output: \( \overline{A} \cdot B \)
4. **Final OR Gate:**
- Inputs: Output of previous OR Gate \( (B + C) \) and output of the AND Gate \( (\overline{A} \cdot B) \)
- Output: \( \overline{A} \cdot B + (B + C) \)
Thus, the overall Boolean expression for the circuit is:
\[ \overline{A} \cdot B + B + C \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F29d14185-3740-4cf8-89ba-8a2b3461623a%2F1db42421-2545-4049-85fe-ca73c27a1245%2Fj3nf8rl_processed.png&w=3840&q=75)
Transcribed Image Text:**Question 13: Give the Boolean expression for the following circuit diagram.**
**Circuit Diagram Explanation:**
The circuit diagram contains the following logic gates:
1. **NOT Gate:**
- Input: A
- Output: \( \overline{A} \)
2. **OR Gate:**
- Inputs: B and C
- Output: \( B + C \)
3. **AND Gate:**
- Inputs: Output of NOT Gate \( (\overline{A}) \) and B
- Output: \( \overline{A} \cdot B \)
4. **Final OR Gate:**
- Inputs: Output of previous OR Gate \( (B + C) \) and output of the AND Gate \( (\overline{A} \cdot B) \)
- Output: \( \overline{A} \cdot B + (B + C) \)
Thus, the overall Boolean expression for the circuit is:
\[ \overline{A} \cdot B + B + C \]
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