Defining a gate as a 2 input function, what is the minimum number of gates needed to implement the following boolean equation? ((A or B) and C) and (A and not ( )

Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
icon
Related questions
Question

Need help with this. Please.

**Question:**

Defining a gate as a 2-input function, what is the minimum number of gates needed to implement the following Boolean equation?

\[
((A \text{ or } B) \text{ and } C) \text{ and } (A \text{ and not } C)
\]

**Pick one of the choices:**

- 0
- 1
- 2
- 4
- 5

**Explanation:**

To solve this problem, analyze the Boolean equation:

1. **(A or B) and C**: This part requires 2 gates:
   - Use an OR gate to calculate (A or B).
   - Use an AND gate to combine ((A or B) and C).

2. **A and not C**: This part requires 2 gates:
   - Use a NOT gate to invert C.
   - Use an AND gate to combine (A and not C).

3. Finally, combine the outputs of the two parts using an AND gate.

Therefore, the minimum number of gates needed is 5:
- 1 OR gate
- 3 AND gates
- 1 NOT gate
Transcribed Image Text:**Question:** Defining a gate as a 2-input function, what is the minimum number of gates needed to implement the following Boolean equation? \[ ((A \text{ or } B) \text{ and } C) \text{ and } (A \text{ and not } C) \] **Pick one of the choices:** - 0 - 1 - 2 - 4 - 5 **Explanation:** To solve this problem, analyze the Boolean equation: 1. **(A or B) and C**: This part requires 2 gates: - Use an OR gate to calculate (A or B). - Use an AND gate to combine ((A or B) and C). 2. **A and not C**: This part requires 2 gates: - Use a NOT gate to invert C. - Use an AND gate to combine (A and not C). 3. Finally, combine the outputs of the two parts using an AND gate. Therefore, the minimum number of gates needed is 5: - 1 OR gate - 3 AND gates - 1 NOT gate
Expert Solution
Step 1 Summary

I have provided  answer  with breif explanation in step  2

I have provided  complete circuit screenshot  in step 3

steps

Step by step

Solved in 3 steps with 1 images

Blurred answer
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Computer Networking: A Top-Down Approach (7th Edi…
Computer Networking: A Top-Down Approach (7th Edi…
Computer Engineering
ISBN:
9780133594140
Author:
James Kurose, Keith Ross
Publisher:
PEARSON
Computer Organization and Design MIPS Edition, Fi…
Computer Organization and Design MIPS Edition, Fi…
Computer Engineering
ISBN:
9780124077263
Author:
David A. Patterson, John L. Hennessy
Publisher:
Elsevier Science
Network+ Guide to Networks (MindTap Course List)
Network+ Guide to Networks (MindTap Course List)
Computer Engineering
ISBN:
9781337569330
Author:
Jill West, Tamara Dean, Jean Andrews
Publisher:
Cengage Learning
Concepts of Database Management
Concepts of Database Management
Computer Engineering
ISBN:
9781337093422
Author:
Joy L. Starks, Philip J. Pratt, Mary Z. Last
Publisher:
Cengage Learning
Prelude to Programming
Prelude to Programming
Computer Engineering
ISBN:
9780133750423
Author:
VENIT, Stewart
Publisher:
Pearson Education
Sc Business Data Communications and Networking, T…
Sc Business Data Communications and Networking, T…
Computer Engineering
ISBN:
9781119368830
Author:
FITZGERALD
Publisher:
WILEY