Homework Help is Here – Start Your Trial Now!
Engineering
Computer Engineering
Use K-map to create the Boolean function (based on 3 variables X,Y,Z) in POS; Draw logical diagram using logical gates. YZ 00 01 11 10 1

Use K-map to create the Boolean function (based on 3 variables X,Y,Z) in POS; Draw logical diagram using logical gates. YZ 00 01 11 10 1

Computer Networking: A Top-Down Approach (7th Edition)
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...
See similar textbooks
icon
Related questions
Question
### Boolean Function Creation Using a K-map **Instruction:** Use a Karnaugh map (K-map) to create the Boolean function (based on 3 variables X, Y, Z) in Product of Sums (POS) form; Draw a logical diagram using logical gates. **K-map Explanation:** The given K-map is a 3-variable map with variables X, Y, and Z. The cell arrangement for YZ across the top is in Gray code order: 00, 01, 11, 10. **K-map Details:** | YZ | 00 | 01 | 11 | 10 | |:----:|:--:|:--:|:--:|:--:| | **X**=0 | 0 | 0 | 0 | 0 | | **X**=1 | 0 | | | | - Each cell represents a minterm. The value inside the cell shows whether the minterm is included (1) or not included (0) in the function. - The top row corresponds to X=0, and the bottom row corresponds to X=1. - Since all cells containing zeros are present, the POS expression will be derived by identifying common variables across zeros. **POS Expression Derivation:** 1. **From X=0 row (covering all columns):** - (X' + Y + Z) - (X' + Y' + Z) - (X' + Y' + Z') - (X' + Y + Z') Since all outputs are zero for X=0, all combinations of Y and Z with X=0 need to be considered. 2. **From X=1 row (only one zero is marked, at 00 position):** - (X + Y + Z) **Logical Diagram:** To draw the logical diagram using gates: - Each POS term represents an OR gate. - All terms are combined using an AND gate. Final POS Expression: - (X' + Y + Z)(X' + Y' + Z)(X' + Y' + Z')(X' + Y + Z')(X + Y + Z) Create OR gates for each term and combine their outputs using an AND gate to form the logical diagram.
Transcribed Image Text:### Boolean Function Creation Using a K-map **Instruction:** Use a Karnaugh map (K-map) to create the Boolean function (based on 3 variables X, Y, Z) in Product of Sums (POS) form; Draw a logical diagram using logical gates. **K-map Explanation:** The given K-map is a 3-variable map with variables X, Y, and Z. The cell arrangement for YZ across the top is in Gray code order: 00, 01, 11, 10. **K-map Details:** | YZ | 00 | 01 | 11 | 10 | |:----:|:--:|:--:|:--:|:--:| | **X**=0 | 0 | 0 | 0 | 0 | | **X**=1 | 0 | | | | - Each cell represents a minterm. The value inside the cell shows whether the minterm is included (1) or not included (0) in the function. - The top row corresponds to X=0, and the bottom row corresponds to X=1. - Since all cells containing zeros are present, the POS expression will be derived by identifying common variables across zeros. **POS Expression Derivation:** 1. **From X=0 row (covering all columns):** - (X' + Y + Z) - (X' + Y' + Z) - (X' + Y' + Z') - (X' + Y + Z') Since all outputs are zero for X=0, all combinations of Y and Z with X=0 need to be considered. 2. **From X=1 row (only one zero is marked, at 00 position):** - (X + Y + Z) **Logical Diagram:** To draw the logical diagram using gates: - Each POS term represents an OR gate. - All terms are combined using an AND gate. Final POS Expression: - (X' + Y + Z)(X' + Y' + Z)(X' + Y' + Z')(X' + Y + Z')(X + Y + Z) Create OR gates for each term and combine their outputs using an AND gate to form the logical diagram.
Expert Solution
Step 1

To draw a logic diagram using K MAP

steps

Step by step

Solved in 3 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
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
SEE MORE TEXTBOOKS