Design a circuit using AND gates to show A+B. Explain.
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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Transcribed Image Text:**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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