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Find the prime implicants for the following Boolean functions, and determine which are essential: (a) F (w, x, y, z) = E(0, 2, 4, 5, 6, 7, 8, 10, 13, 15) (b) F (A, B, C, D) = E(0, 2, 3, 5, 7, 8, 10, 11, 14, 15) %3D (c) F (A, B, C, D) = E(1, 3, 4, 5, 10, 11, 12, 13, 14, 15)

Find the prime implicants for the following Boolean functions, and determine which are essential: (a) F (w, x, y, z) = E(0, 2, 4, 5, 6, 7, 8, 10, 13, 15) (b) F (A, B, C, D) = E(0, 2, 3, 5, 7, 8, 10, 11, 14, 15) %3D (c) F (A, B, C, D) = E(1, 3, 4, 5, 10, 11, 12, 13, 14, 15)

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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**Task: Find the Prime Implicants for Boolean Functions** **Objective:** Determine the prime implicants and identify essential ones for the given Boolean functions. **Functions:** (a) \( F(w, x, y, z) = \Sigma(0, 2, 4, 5, 6, 7, 8, 10, 13, 15) \) (b) \( F(A, B, C, D) = \Sigma(0, 2, 3, 5, 7, 8, 10, 11, 14, 15) \) (c) \( F(A, B, C, D) = \Sigma(1, 3, 4, 5, 10, 11, 12, 13, 14, 15) \) **Instructions:** - **Prime Implicants:** These are the simplest form terms that can be combined to cover all the minterms without redundancy. - **Essential Prime Implicants:** These are prime implicants that cover one or more minterms that no other prime implicant covers. Identifying these is crucial for minimizing the logical expression. **Approach:** 1. **List the given minterms** for each function. 2. **Group the minterms** by the number of 1s in their binary representation. 3. **Combine pairs** to simplify and form larger groups. 4. **Identify prime implicants** from these groups. 5. **Determine essential prime implicants** that cover unique minterms. Adopting this process will aid in optimizing Boolean functions for logic circuit design efficiently.
Transcribed Image Text:**Task: Find the Prime Implicants for Boolean Functions** **Objective:** Determine the prime implicants and identify essential ones for the given Boolean functions. **Functions:** (a) \( F(w, x, y, z) = \Sigma(0, 2, 4, 5, 6, 7, 8, 10, 13, 15) \) (b) \( F(A, B, C, D) = \Sigma(0, 2, 3, 5, 7, 8, 10, 11, 14, 15) \) (c) \( F(A, B, C, D) = \Sigma(1, 3, 4, 5, 10, 11, 12, 13, 14, 15) \) **Instructions:** - **Prime Implicants:** These are the simplest form terms that can be combined to cover all the minterms without redundancy. - **Essential Prime Implicants:** These are prime implicants that cover one or more minterms that no other prime implicant covers. Identifying these is crucial for minimizing the logical expression. **Approach:** 1. **List the given minterms** for each function. 2. **Group the minterms** by the number of 1s in their binary representation. 3. **Combine pairs** to simplify and form larger groups. 4. **Identify prime implicants** from these groups. 5. **Determine essential prime implicants** that cover unique minterms. Adopting this process will aid in optimizing Boolean functions for logic circuit design efficiently.
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