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7. Give the number of prime implicants (PI), number of distinguished 1-cells, and essential prime implicants (EPI) for the following K-maps: Recall the implicant terms: • Implicant Bubble covering only 1s (size of bubble must be a power of 2). Prime implicant Bubble that is expanded as big as possible (but increases in size by powers of 2). Essential prime implicant Bubble that contains a 1 covered only by itself and no other prime implicant bubble. • Non-essential prime implicant A 1 that can be bubbled by more then one prime implicant bubble. Е. АВ C D 00 0 1 11 10 0 0 1 1 01 1 11 1) 10 1

7. Give the number of prime implicants (PI), number of distinguished 1-cells, and essential prime implicants (EPI) for the following K-maps: Recall the implicant terms: • Implicant Bubble covering only 1s (size of bubble must be a power of 2). Prime implicant Bubble that is expanded as big as possible (but increases in size by powers of 2). Essential prime implicant Bubble that contains a 1 covered only by itself and no other prime implicant bubble. • Non-essential prime implicant A 1 that can be bubbled by more then one prime implicant bubble. Е. АВ C D 00 0 1 11 10 0 0 1 1 01 1 11 1) 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...
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Draw the K-Map with the groupings and just indicate the number of distinguished 1-cells and EPIs.

 

--- ### Prime Implicants and K-Maps #### 7. Task: Determine the number of prime implicants (PI), distinguished 1-cells, and essential prime implicants (EPI) for the given Karnaugh maps (K-maps). #### Implicant Terminology: - **Implicant**: - A bubble covering only 1s (each bubble must be a power of 2 in size). - **Prime Implicant**: - A bubble expanded to the largest possible size (while maintaining powers of 2). - **Essential Prime Implicant**: - A bubble containing a 1 covered exclusively by it and not by any other prime implicant bubble. - **Non-essential Prime Implicant**: - A 1 that can be covered by multiple prime implicant bubbles. #### Explanation of the Diagram (K-map E): - The K-map is labeled with variables A, B on the top and C, D on the side. Each cell represents a binary combination of these variables. - Cells containing the value "1" have been circled in red. These circles represent the implicants. - The K-map layout is as follows: ``` AB \ 00 01 11 10 CD 00 0 1 1 0 01 1 0 1 0 11 1 1 0 1 10 1 0 0 1 ``` - Red circles highlight the following cells: - (C=0,D=1; A=0,B=1) - (C=0,D=0; A=0,B=1) - (C=1,D=1; A=0,B=0) - (C=1,D=1; A=1,B=0) - (C=1,D=0; A=0,B=0) - Others as covered in the layout. Each circle represents an implicant that can potentially be a prime implicant or essential depending on overlap and coverage by other red circles.
Transcribed Image Text:--- ### Prime Implicants and K-Maps #### 7. Task: Determine the number of prime implicants (PI), distinguished 1-cells, and essential prime implicants (EPI) for the given Karnaugh maps (K-maps). #### Implicant Terminology: - **Implicant**: - A bubble covering only 1s (each bubble must be a power of 2 in size). - **Prime Implicant**: - A bubble expanded to the largest possible size (while maintaining powers of 2). - **Essential Prime Implicant**: - A bubble containing a 1 covered exclusively by it and not by any other prime implicant bubble. - **Non-essential Prime Implicant**: - A 1 that can be covered by multiple prime implicant bubbles. #### Explanation of the Diagram (K-map E): - The K-map is labeled with variables A, B on the top and C, D on the side. Each cell represents a binary combination of these variables. - Cells containing the value "1" have been circled in red. These circles represent the implicants. - The K-map layout is as follows: ``` AB \ 00 01 11 10 CD 00 0 1 1 0 01 1 0 1 0 11 1 1 0 1 10 1 0 0 1 ``` - Red circles highlight the following cells: - (C=0,D=1; A=0,B=1) - (C=0,D=0; A=0,B=1) - (C=1,D=1; A=0,B=0) - (C=1,D=1; A=1,B=0) - (C=1,D=0; A=0,B=0) - Others as covered in the layout. Each circle represents an implicant that can potentially be a prime implicant or essential depending on overlap and coverage by other red circles.
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