**Explain this circuit in detail****NOT gate using NAND gate:**In the provided diagram, two circuits are illustrated. Both circuits achieve the function of a NOT gate, but one uses a traditional NOT gate, and the other uses a NAND gate to create the NOT gate functionality. 1. **Top Circuit (Standard NOT Gate):** - The circuit includes one switch labeled as input \( A \). - The switch is connected to a NOT gate. - The output from the NOT gate, labeled \( A' \), is connected to a light bulb. - When the switch \( A \) is turned on (logic level 1), the NOT gate inverts this to logic level 0, turning the light bulb off. - When the switch \( A \) is turned off (logic level 0), the NOT gate inverts this to logic level 1, turning the light bulb on.2. **Bottom Circuit (NOT Gate using NAND Gate):** - The circuit includes one switch labeled as input \( A \). - The switch is connected to both inputs of a NAND gate. - The output from the NAND gate, labeled \( A' \), is connected to a light bulb. - Since a NAND gate outputs logic level 0 only when both inputs are at logic level 1: - When the switch \( A \) is turned on (logic level 1), both inputs of the NAND gate are at logic level 1, producing an output of logic level 0, and thus the light bulb turns off. - When the switch \( A \) is turned off (logic level 0), both inputs of the NAND gate are at logic level 0, producing an output of logic level 1, and thus the light bulb turns on.**Summary:**Both circuits effectively demonstrate how a NOT gate functions, but the bottom circuit shows how a NAND gate can be used to replicate the behavior of a NOT gate by connecting both of its inputs to the same signal. This substitution is a fundamental concept in digital logic design, illustrating the versatility and importance of the NAND gate in building other basic logic gates. ## OR Gate Using NAND Gate### ExplanationThis section details the construction of an OR gate utilizing NAND gates. Below is a step-by-step breakdown of the circuit diagram shown:#### Components:- Inputs: A, B- NAND Gates- Inverters- Outputs: A', B', A + B (Light bulbs as indicator)#### Circuit Description:1. **Inputs (A and B):** - There are two main inputs labeled A and B. These values will be used to determine the output of the OR gate.2. **Inverters:** - The first part of the circuit involves two inverters connected to inputs A and B, respectively. These inverters generate the inverted signals A' and B'. - The inverted output of A is labeled as A'. - The inverted output of B is labeled as B'.3. **NAND Gates:** - The circuit then routes the signals as follows: - The input A and B are each passed through their respective inverters to create A' and B’. - The output from these inverters (A' and B') are passed to another NAND gate. 4. **Output:** - The output of the final NAND gate is used to drive the light bulb, which represents the OR operation result (A + B). - This approach effectively realizes the OR operation through a combination of NAND gates and inverters. The light bulb will illuminate if either input A OR input B (or both) is true.By using these NAND gates and inverters, the circuit successfully emulates the behavior of an OR gate. The core idea behind this logic circuit lies in De Morgan's Theorem.

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Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

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Question

**Explain this circuit in detail**

**NOT gate using NAND gate:**

In the provided diagram, two circuits are illustrated. Both circuits achieve the function of a NOT gate, but one uses a traditional NOT gate, and the other uses a NAND gate to create the NOT gate functionality.

1. **Top Circuit (Standard NOT Gate):**
- The circuit includes one switch labeled as input \( A \).
- The switch is connected to a NOT gate.
- The output from the NOT gate, labeled \( A' \), is connected to a light bulb.
- When the switch \( A \) is turned on (logic level 1), the NOT gate inverts this to logic level 0, turning the light bulb off.
- When the switch \( A \) is turned off (logic level 0), the NOT gate inverts this to logic level 1, turning the light bulb on.

2. **Bottom Circuit (NOT Gate using NAND Gate):**
- The circuit includes one switch labeled as input \( A \).
- The switch is connected to both inputs of a NAND gate.
- The output from the NAND gate, labeled \( A' \), is connected to a light bulb.
- Since a NAND gate outputs logic level 0 only when both inputs are at logic level 1:
- When the switch \( A \) is turned on (logic level 1), both inputs of the NAND gate are at logic level 1, producing an output of logic level 0, and thus the light bulb turns off.
- When the switch \( A \) is turned off (logic level 0), both inputs of the NAND gate are at logic level 0, producing an output of logic level 1, and thus the light bulb turns on.

**Summary:**
Both circuits effectively demonstrate how a NOT gate functions, but the bottom circuit shows how a NAND gate can be used to replicate the behavior of a NOT gate by connecting both of its inputs to the same signal. This substitution is a fundamental concept in digital logic design, illustrating the versatility and importance of the NAND gate in building other basic logic gates.

## OR Gate Using NAND Gate

### Explanation

This section details the construction of an OR gate utilizing NAND gates. Below is a step-by-step breakdown of the circuit diagram shown:

#### Components:
- Inputs: A, B
- NAND Gates
- Inverters
- Outputs: A', B', A + B (Light bulbs as indicator)

#### Circuit Description:
1. **Inputs (A and B):**
- There are two main inputs labeled A and B. These values will be used to determine the output of the OR gate.

2. **Inverters:**
- The first part of the circuit involves two inverters connected to inputs A and B, respectively. These inverters generate the inverted signals A' and B'.
- The inverted output of A is labeled as A'.
- The inverted output of B is labeled as B'.

3. **NAND Gates:**
- The circuit then routes the signals as follows:
- The input A and B are each passed through their respective inverters to create A' and B’.
- The output from these inverters (A' and B') are passed to another NAND gate.

4. **Output:**
- The output of the final NAND gate is used to drive the light bulb, which represents the OR operation result (A + B).
- This approach effectively realizes the OR operation through a combination of NAND gates and inverters. The light bulb will illuminate if either input A OR input B (or both) is true.

By using these NAND gates and inverters, the circuit successfully emulates the behavior of an OR gate. The core idea behind this logic circuit lies in De Morgan's Theorem.

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