fi2 = a' fi3 = a' + b a' + b' 14
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...
Related questions
Question
100%
Prove the validity of the following set of functions, reduced to minimum SOP form:
(Use table)
![**Table 2.13: All Two-Variable Functions**
This table represents all possible functions of two variables, \(a\) and \(b\), resulting in multiple output functions \(f_0\) to \(f_{15}\). Each column under \(f_i\) (where \(i = 0, 1, \ldots, 15\)) specifies the output of the function for the given inputs \(a\) and \(b\).
**Table Details:**
- **Inputs:**
- \(a\) and \(b\) can each be either 0 or 1.
- The four possible combinations of these inputs are listed in the two leftmost columns.
- **Outputs:**
- The remaining columns \(f_0\) to \(f_{15}\) represent all possible outputs for the given inputs of \(a\) and \(b\).
- Each \(f_i\) column provides a binary result corresponding to each input combination:
- \(f_0: [0, 0, 0, 0]\)
- \(f_1: [0, 0, 0, 1]\)
- \(f_2: [0, 0, 1, 0]\)
- \(f_3: [0, 0, 1, 1]\)
- \(f_4: [0, 1, 0, 0]\)
- \(f_5: [0, 1, 0, 1]\)
- \(f_6: [0, 1, 1, 0]\)
- \(f_7: [0, 1, 1, 1]\)
- \(f_8: [1, 0, 0, 0]\)
- \(f_9: [1, 0, 0, 1]\)
- \(f_{10}: [1, 0, 1, 0]\)
- \(f_{11}: [1, 0, 1, 1]\)
- \(f_{12}: [1, 1, 0, 0]\)
- \(f_{13}: [1, 1, 0, 1]\)
- \(f_{14}: [1, 1, 1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F09add7e4-1de4-4c46-9eb6-cd08d3786f74%2F7d9df1b3-f7b9-48d1-9d94-c94a5ccd39fd%2Flgpg8ck_processed.png&w=3840&q=75)
Transcribed Image Text:**Table 2.13: All Two-Variable Functions**
This table represents all possible functions of two variables, \(a\) and \(b\), resulting in multiple output functions \(f_0\) to \(f_{15}\). Each column under \(f_i\) (where \(i = 0, 1, \ldots, 15\)) specifies the output of the function for the given inputs \(a\) and \(b\).
**Table Details:**
- **Inputs:**
- \(a\) and \(b\) can each be either 0 or 1.
- The four possible combinations of these inputs are listed in the two leftmost columns.
- **Outputs:**
- The remaining columns \(f_0\) to \(f_{15}\) represent all possible outputs for the given inputs of \(a\) and \(b\).
- Each \(f_i\) column provides a binary result corresponding to each input combination:
- \(f_0: [0, 0, 0, 0]\)
- \(f_1: [0, 0, 0, 1]\)
- \(f_2: [0, 0, 1, 0]\)
- \(f_3: [0, 0, 1, 1]\)
- \(f_4: [0, 1, 0, 0]\)
- \(f_5: [0, 1, 0, 1]\)
- \(f_6: [0, 1, 1, 0]\)
- \(f_7: [0, 1, 1, 1]\)
- \(f_8: [1, 0, 0, 0]\)
- \(f_9: [1, 0, 0, 1]\)
- \(f_{10}: [1, 0, 1, 0]\)
- \(f_{11}: [1, 0, 1, 1]\)
- \(f_{12}: [1, 1, 0, 0]\)
- \(f_{13}: [1, 1, 0, 1]\)
- \(f_{14}: [1, 1, 1
Transcribed Image Text:The image displays a set of mathematical equations:
1. \( f_{12} = a' \)
2. \( f_{13} = a' + b \)
3. \( f_{14} = a' + b' \)
4. \( f_{15} = 1 \)
These equations appear to define a series of functions or mappings, utilizing variables indicated by prime notations and constants. There are no graphs or diagrams included in the image.
Expert Solution
Step 1
Proved the validity of the given set of functions to minimum SOP form
Step by step
Solved in 2 steps with 1 images
Recommended textbooks for you
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 Engineering
ISBN:
9780124077263
Author:
David A. Patterson, John L. Hennessy
Publisher:
Elsevier Science
Network+ Guide to Networks (MindTap Course List)
Computer Engineering
ISBN:
9781337569330
Author:
Jill West, Tamara Dean, Jean Andrews
Publisher:
Cengage Learning
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 Engineering
ISBN:
9780124077263
Author:
David A. Patterson, John L. Hennessy
Publisher:
Elsevier Science
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
Computer Engineering
ISBN:
9781337093422
Author:
Joy L. Starks, Philip J. Pratt, Mary Z. Last
Publisher:
Cengage Learning
Prelude to Programming
Computer Engineering
ISBN:
9780133750423
Author:
VENIT, Stewart
Publisher:
Pearson Education
Sc Business Data Communications and Networking, T…
Computer Engineering
ISBN:
9781119368830
Author:
FITZGERALD
Publisher:
WILEY