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: PEARSON
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Computer Architecture question Could you draw the k-map and sum the product terms. I have provided an example. Thank you.
**2. SOP Form** Given: \( Z = \sum A, B, C(0, 1, 6, 7) \) a. **K-map** b. **Sum the Product Terms** - Final Expression: In this exercise, we use the SOP (Sum of Products) form to simplify the Boolean expression of the function \( Z \). The input variables are A, B, and C, and the minterms are listed as 0, 1, 6, and 7. We construct a Karnaugh map (K-map) for visual simplification, and then use it to identify and sum the product terms to derive the final simplified expression.
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Transcribed Image Text:**2. SOP Form** Given: \( Z = \sum A, B, C(0, 1, 6, 7) \) a. **K-map** b. **Sum the Product Terms** - Final Expression: In this exercise, we use the SOP (Sum of Products) form to simplify the Boolean expression of the function \( Z \). The input variables are A, B, and C, and the minterms are listed as 0, 1, 6, and 7. We construct a Karnaugh map (K-map) for visual simplification, and then use it to identify and sum the product terms to derive the final simplified expression.
**Example** 1. **SOP form,** \( Z = \Sigma A, B, C (1, 3, 6, 7) \) a. **K-map** The K-map (Karnaugh map) is shown for three variables, \( A \), \( B \), and \( C \). The layout is as follows: - Across the top, the columns are labeled under the heading \( BC \): - \( B'C' \) (00) - \( B'C \) (01) - \( BC \) (11) - \( BC' \) (10) - Down the side, the rows are labeled as: - \( A' \), row for \( A = 0 \) - \( A \), row for \( A = 1 \) The cells within the K-map are filled with binary values as follows: \[ \begin{array}{c|c|c|c|c} & B'C' & B'C & BC & BC' \\ \hline A' & 0 & 1 & 1 & 0 \\ \hline A & 0 & 0 & 1 & 1 \\ \end{array} \] - Groupings are indicated on the K-map: - **Red Group:** Includes cells (01) and (11) from the first row, corresponding to minterms 1 and 3. - **Green Group:** Includes cells (11) and (10) from the second row, corresponding to minterms 6 and 7. b. **Sum the product terms**: i. From the red group, the product term is \( A'C \). ii. From the green group, the product term is \( AB \). iii. The final expression is the sum of these products: \( A'C + AB \).
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Transcribed Image Text:**Example** 1. **SOP form,** \( Z = \Sigma A, B, C (1, 3, 6, 7) \) a. **K-map** The K-map (Karnaugh map) is shown for three variables, \( A \), \( B \), and \( C \). The layout is as follows: - Across the top, the columns are labeled under the heading \( BC \): - \( B'C' \) (00) - \( B'C \) (01) - \( BC \) (11) - \( BC' \) (10) - Down the side, the rows are labeled as: - \( A' \), row for \( A = 0 \) - \( A \), row for \( A = 1 \) The cells within the K-map are filled with binary values as follows: \[ \begin{array}{c|c|c|c|c} & B'C' & B'C & BC & BC' \\ \hline A' & 0 & 1 & 1 & 0 \\ \hline A & 0 & 0 & 1 & 1 \\ \end{array} \] - Groupings are indicated on the K-map: - **Red Group:** Includes cells (01) and (11) from the first row, corresponding to minterms 1 and 3. - **Green Group:** Includes cells (11) and (10) from the second row, corresponding to minterms 6 and 7. b. **Sum the product terms**: i. From the red group, the product term is \( A'C \). ii. From the green group, the product term is \( AB \). iii. The final expression is the sum of these products: \( A'C + AB \).
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Sum of Product form is a Boolean Algebra expression in which different product terms from inputs are summed together.

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