Database System Concepts
7th Edition
ISBN: 9780078022159
Author: Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher: McGraw-Hill Education
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Computer Architecture Question:
1. Could you show the red & green when drawing the k-map.
2. Sum the product terms i,ii,iii
The answer should look like the example I provided in the picture.
Thank you.
Transcribed Image Text:### Example
1. **SOP form, Z**
- \( Z = \Sigma A, B, C (1, 3, 6, 7) \)
a. **K-map**
This is a Karnaugh map (K-map) used to simplify the Boolean expression. It is a grid representing possible values of variables A, B, and C.
- **Grid Layout:**
- Columns are labeled as \( B'C', B'C, BC, BC' \) with binary numbers 00, 01, 11, 10.
- Rows are labeled as \( A'0, A1 \).
- **Values in Cells:**
- The K-map cells contain the following values:
1. \( A'B'C = 1 \)
2. \( A'BC' = 1 \)
3. \( ABC = 1 \)
4. \( ABC' = 1 \)
- **Grouping (shown by rectangles):**
- **Red Group:** Encloses cells \( A'B'C \) and \( A'BC' \) (producing the term \( A'C \)).
- **Green Group:** Encloses cells \( ABC \) and \( ABC' \) (producing the term \( AB \)).
b. **Sum the product terms:**
i. **From red group, product term:** \( A'C \)
ii. **From green group, product term:** \( AB \)
iii. **Final expression:** \( A'C + AB \)
This exercise uses a K-map to minimize the logic expression \( Z \) using the Sum of Products (SOP) method, resulting in the simplified expression \( A'C + AB \).
Transcribed Image Text:1. **SOP form,** \(Z = \Sigma A, B, C (2, 4, 5, 6)\)
a. **K-map**
b. **Sum the product terms**
**Final expression:**
Expert Solution
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a. K-map
1. SOP form, Z = A,B,C (2, 4, 5, 6)
a. K-map
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