Draw the K-Map with the groupings and just indicate the number of distinguished 1-cells and EPIs.

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Draw the K-Map with the groupings and just indicate the number of distinguished 1-cells and EPIs.

 

# K-map Analysis for Prime Implicants

This section explains how to determine the number of prime implicants (PI), number of distinguished 1-cells, and essential prime implicants (EPI) in Karnaugh maps (K-maps). 

### Key Terminology

- **Implicant:** A bubble covering only 1s, with the size of the bubble being a power of 2.
  
- **Prime Implicant:** A bubble expanded as large as possible, incrementing in size by powers of 2.

- **Essential Prime Implicant:** A bubble containing a 1 covered uniquely by itself and not by any other prime implicant bubble.
  
- **Non-essential Prime Implicant:** A 1 that can be part of multiple prime implicant bubbles.

### K-map Example

#### Grid Explanation

- The K-map grid has the variables A, B across the top and C, D along the side.
- The grid is a 4x4 matrix of cells corresponding to different combinations of A, B, C, and D values.

#### Details of the Bubbles

1. **Blue Bubbles:**
   - Encloses groups of adjacent 1s, forming the largest possible rectangles following powers of 2 (e.g., groups of 1, 2, 4, or 8).
   - Number of blue prime implicants is shown by different clusters:
     - One vertical line covers two groups of 1s in the middle columns.
     - Another horizontal line connects groups of 1s at the bottom row.

2. **Black Bubbles:**
   - Highlights essential prime implicants.
   - Contains individual 1s that cannot be grouped into larger groups without overextending into unnecessary zeros.

By identifying these bubbles, we can systematically determine prime and essential implicants. This helps in simplifying boolean expressions efficiently.
Transcribed Image Text:# K-map Analysis for Prime Implicants This section explains how to determine the number of prime implicants (PI), number of distinguished 1-cells, and essential prime implicants (EPI) in Karnaugh maps (K-maps). ### Key Terminology - **Implicant:** A bubble covering only 1s, with the size of the bubble being a power of 2. - **Prime Implicant:** A bubble expanded as large as possible, incrementing in size by powers of 2. - **Essential Prime Implicant:** A bubble containing a 1 covered uniquely by itself and not by any other prime implicant bubble. - **Non-essential Prime Implicant:** A 1 that can be part of multiple prime implicant bubbles. ### K-map Example #### Grid Explanation - The K-map grid has the variables A, B across the top and C, D along the side. - The grid is a 4x4 matrix of cells corresponding to different combinations of A, B, C, and D values. #### Details of the Bubbles 1. **Blue Bubbles:** - Encloses groups of adjacent 1s, forming the largest possible rectangles following powers of 2 (e.g., groups of 1, 2, 4, or 8). - Number of blue prime implicants is shown by different clusters: - One vertical line covers two groups of 1s in the middle columns. - Another horizontal line connects groups of 1s at the bottom row. 2. **Black Bubbles:** - Highlights essential prime implicants. - Contains individual 1s that cannot be grouped into larger groups without overextending into unnecessary zeros. By identifying these bubbles, we can systematically determine prime and essential implicants. This helps in simplifying boolean expressions efficiently.
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