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 ( )
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
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Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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![**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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6d1ae07f-bdb5-47a8-9afa-ea5a04bdf9c8%2Fc1a0488f-67fd-472e-acfe-23e333e3851a%2Fq3dpl9k_processed.jpeg&w=3840&q=75)
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
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