Introductory Circuit Analysis (13th Edition)
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ISBN: 9780133923605
Author: Robert L. Boylestad
Publisher: PEARSON
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![**Problem 5:**
**Objective:** Find the minimum Sum of Products (SOP) solution for the function F.
**Function Definition:**
\[ F = \Sigma wxyz (0, 1, 2, 5, 7, 8, 9, 10) \]
**Solution Area:**
F = ___________
**Explanation of the Diagram:**
The diagram is a 4-variable Karnaugh map used for simplifying Boolean expressions. The variables involved are \( w, x, y, \) and \( z \). The map is organized in a 4 x 4 grid, corresponding to the combinations of these variables.
- **Axes Labels**:
- The top side is labeled \( WX \) and shows combinations as binary pairs: \( 00, 01, 11, 10 \).
- The left side is labeled \( YZ \) with binary pairs: \( 00, 01, 11, 10 \).
- **Grid Entries**:
- Each cell contains a number representing a minterm number. Only the minterms listed in the function \( F \) have significant values:
- Minterms: 0, 1, 2, 5, 7, 8, 9, 10
- The numbers within grid cells directly correspond to these minterms:
- Cell \( (00, 00) \) - Minterm 0
- Cell \( (01, 00) \) - Minterm 1
- Cell \( (10, 00) \) - Minterm 2
- Cell \( (01, 01) \) - Minterm 5
- Cell \( (11, 01) \) - Minterm 7
- Cell \( (00, 10) \) - Minterm 8
- Cell \( (01, 10) \) - Minterm 9
- Cell \( (10, 10) \) - Minterm 10
**Purpose of the Karnaugh Map:**
The map is used to visually simplify the logic equation by grouping adjacent cells with 1s (the minterms), allowing for reduction using Boolean algebra rules. This process leads to the simplest Sum of Products form of the function.](https://content.bartleby.com/qna-images/question/93e18a88-13ba-47d2-8c84-ec9d29397d2a/442aa79e-2e5f-40bf-a1df-58d5b3ab0654/8spwkk_processed.jpeg)
Transcribed Image Text:**Problem 5:**
**Objective:** Find the minimum Sum of Products (SOP) solution for the function F.
**Function Definition:**
\[ F = \Sigma wxyz (0, 1, 2, 5, 7, 8, 9, 10) \]
**Solution Area:**
F = ___________
**Explanation of the Diagram:**
The diagram is a 4-variable Karnaugh map used for simplifying Boolean expressions. The variables involved are \( w, x, y, \) and \( z \). The map is organized in a 4 x 4 grid, corresponding to the combinations of these variables.
- **Axes Labels**:
- The top side is labeled \( WX \) and shows combinations as binary pairs: \( 00, 01, 11, 10 \).
- The left side is labeled \( YZ \) with binary pairs: \( 00, 01, 11, 10 \).
- **Grid Entries**:
- Each cell contains a number representing a minterm number. Only the minterms listed in the function \( F \) have significant values:
- Minterms: 0, 1, 2, 5, 7, 8, 9, 10
- The numbers within grid cells directly correspond to these minterms:
- Cell \( (00, 00) \) - Minterm 0
- Cell \( (01, 00) \) - Minterm 1
- Cell \( (10, 00) \) - Minterm 2
- Cell \( (01, 01) \) - Minterm 5
- Cell \( (11, 01) \) - Minterm 7
- Cell \( (00, 10) \) - Minterm 8
- Cell \( (01, 10) \) - Minterm 9
- Cell \( (10, 10) \) - Minterm 10
**Purpose of the Karnaugh Map:**
The map is used to visually simplify the logic equation by grouping adjacent cells with 1s (the minterms), allowing for reduction using Boolean algebra rules. This process leads to the simplest Sum of Products form of the function.
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