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4. SOP form, Z= YA,B,C(3, 4, 6, 7) K-map a. b. Sum the product terms Final expression:

4. SOP form, Z= YA,B,C(3, 4, 6, 7) 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
Problem 1PE
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Computer Architecture: 1. Could you draw a k-map (Please show which one is red and green) 2. Sum the products a. Red group b. Green group c. Final Expression
4. **SOP form, Z = ΣA,B,C(3, 4, 6, 7)** a. **K-map** b. **Sum the product terms** Final expression:
Transcribed Image Text:4. **SOP form, Z = ΣA,B,C(3, 4, 6, 7)** a. **K-map** b. **Sum the product terms** Final expression:
**Example** 1. **SOP form**, \( Z = \sum A, B, C(1, 3, 6, 7) \) a. **K-map** * Diagram Explanation: * A Karnaugh map (K-map) is used here for simplification. * The map is arranged with variables A, B, and C. * The columns are labeled B'C', B'C, BC, and BC', while rows are labeled A'0 and A1. * The cells are filled based on the given minterms (1, 3, 6, 7). * Cells: * Row A'0: Columns B'C' (0), B'C (1), BC (1), BC' (0) * Row A1: Columns B'C' (0), B'C (0), BC (1), BC' (1) * Groupings: * Red Group: Contains minterms 1 and 3, forming a horizontal group. * Green Group: Contains minterms 6 and 7, forming a vertical group. b. **Sum the product terms** i. From the red group, we get the product term \( A'C \). ii. From the green group, we get the product term \( AB \). iii. **Final expression**: \( A'C + AB \)
Transcribed Image Text:**Example** 1. **SOP form**, \( Z = \sum A, B, C(1, 3, 6, 7) \) a. **K-map** * Diagram Explanation: * A Karnaugh map (K-map) is used here for simplification. * The map is arranged with variables A, B, and C. * The columns are labeled B'C', B'C, BC, and BC', while rows are labeled A'0 and A1. * The cells are filled based on the given minterms (1, 3, 6, 7). * Cells: * Row A'0: Columns B'C' (0), B'C (1), BC (1), BC' (0) * Row A1: Columns B'C' (0), B'C (0), BC (1), BC' (1) * Groupings: * Red Group: Contains minterms 1 and 3, forming a horizontal group. * Green Group: Contains minterms 6 and 7, forming a vertical group. b. **Sum the product terms** i. From the red group, we get the product term \( A'C \). ii. From the green group, we get the product term \( AB \). iii. **Final expression**: \( A'C + AB \)
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