**Design a Circuit Using AND Gates to Show A+B. Explain.**The task requires the design of a circuit using only AND gates in order to demonstrate the logical operation A+B (OR operation). OR Operation (A+B): In digital logic, the OR operation outputs true (1) when at least one input is true. The challenge here is to achieve the OR function (A+B) using only AND gates, which naturally perform the AND operation.Explanation:1. **Using De Morgan's Theorems:** - A + B = ¬(¬A ∧ ¬B) - This means A OR B can be implemented by inverting the inputs, performing the AND operation, and then inverting the result.2. **Circuit Diagram:** - **Step 1:** Invert each input (A and B) by using NAND gates twice (because NAND gates act as NOT gates when their inputs are identical). - **Step 2:** AND the results of these operations (using NAND gates as AND gates). - **Step 3:** Invert the result (again using a NAND gate as a NOT gate).**Tools and Software:**For this task, it appears that you might be using a word processor (such as seen in the image with options like 'Edit', 'View', 'Insert', 'Format', 'Tools', 'Table', and various text formatting tools). Use a drawing tool within the word processing software to design the circuit diagram, or consider using specialized circuit design software for a more accurate representation.**Example Layout:**The diagram is not present in the provided image, but here is a textual description of the circuit construction:1. Input A goes into the first NAND gate. The output is A'.2. Input B goes into the second NAND gate. The output is B'.3. The outputs A' and B' go into a third NAND gate. The final output is (A' ∧ B')', which equals A + B.This way of constructing the OR function using only AND gates demonstrates a fundamental principle of digital logic design, showcasing how basic gates can be combined to form more complex operations.

The question is to design a circuit using AND gates to show A+B.

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Design a circuit using AND gates to show A+B. Explain.

Database System Concepts

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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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Question

**Design a Circuit Using AND Gates to Show A+B. Explain.**

The task requires the design of a circuit using only AND gates in order to demonstrate the logical operation A+B (OR operation).

OR Operation (A+B): In digital logic, the OR operation outputs true (1) when at least one input is true. The challenge here is to achieve the OR function (A+B) using only AND gates, which naturally perform the AND operation.

Explanation:

1. **Using De Morgan's Theorems:**
- A + B = ¬(¬A ∧ ¬B)
- This means A OR B can be implemented by inverting the inputs, performing the AND operation, and then inverting the result.

2. **Circuit Diagram:**
- **Step 1:** Invert each input (A and B) by using NAND gates twice (because NAND gates act as NOT gates when their inputs are identical).
- **Step 2:** AND the results of these operations (using NAND gates as AND gates).
- **Step 3:** Invert the result (again using a NAND gate as a NOT gate).

**Tools and Software:**
For this task, it appears that you might be using a word processor (such as seen in the image with options like 'Edit', 'View', 'Insert', 'Format', 'Tools', 'Table', and various text formatting tools). Use a drawing tool within the word processing software to design the circuit diagram, or consider using specialized circuit design software for a more accurate representation.

**Example Layout:**
The diagram is not present in the provided image, but here is a textual description of the circuit construction:
1. Input A goes into the first NAND gate. The output is A'.
2. Input B goes into the second NAND gate. The output is B'.
3. The outputs A' and B' go into a third NAND gate. The final output is (A' ∧ B')', which equals A + B.

This way of constructing the OR function using only AND gates demonstrates a fundamental principle of digital logic design, showcasing how basic gates can be combined to form more complex operations.

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