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
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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:

\[ \overline{A} \cdot B + B + C \]
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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