Homework Help is Here – Start Your Trial Now!
Engineering
Computer Science
Design a circuit using AND gates to show A+B. Explain.

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

Database System Concepts
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
See similar textbooks
icon
Related questions
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.
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.
Expert Solution
steps

Step by step

Solved in 2 steps with 1 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Fundamentals of Boolean Algebra and Digital Logics
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, computer-science and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Database System Concepts
Database System Concepts
Computer Science
ISBN:
9780078022159
Author:
Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:
McGraw-Hill Education
Starting Out with Python (4th Edition)
Starting Out with Python (4th Edition)
Computer Science
ISBN:
9780134444321
Author:
Tony Gaddis
Publisher:
PEARSON
Digital Fundamentals (11th Edition)
Digital Fundamentals (11th Edition)
Computer Science
ISBN:
9780132737968
Author:
Thomas L. Floyd
Publisher:
PEARSON
C How to Program (8th Edition)
C How to Program (8th Edition)
Computer Science
ISBN:
9780133976892
Author:
Paul J. Deitel, Harvey Deitel
Publisher:
PEARSON
Database Systems: Design, Implementation, & Manag…
Database Systems: Design, Implementation, & Manag…
Computer Science
ISBN:
9781337627900
Author:
Carlos Coronel, Steven Morris
Publisher:
Cengage Learning
Programmable Logic Controllers
Programmable Logic Controllers
Computer Science
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education
SEE MORE TEXTBOOKS