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1. SOP form, Z= ΣA,B,C(2, 4, 5, 6) K-map a. b. Sum the product terms Final expression:

1. SOP form, Z= ΣA,B,C(2, 4, 5, 6) K-map a. b. Sum the product terms Final expression:

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
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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.
### 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:### 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 \( A'C + AB \).
1. **SOP form,** \(Z = \Sigma A, B, C (2, 4, 5, 6)\) a. **K-map** b. **Sum the product terms** **Final expression:**
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
a. K-map

1. SOP form, Z = ∑ A,B,C (2, 4, 5, 6)

   a. K-map

 

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