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4. Fill in the Karnaugh map for the function. F = Ew,x,y,z(4, 5, 8,10,13,14,15) + d(2, 9) Find the minimum SOP expression for the function. F = Find the canonical sum F = YZ Y W X 00⁰ 01 11³ 10 1 2 00 01 11 10 12 8 4 5 7 6 13 9 15 W 14 X 11 10 N

4. Fill in the Karnaugh map for the function. F = Ew,x,y,z(4, 5, 8,10,13,14,15) + d(2, 9) Find the minimum SOP expression for the function. F = Find the canonical sum F = YZ Y W X 00⁰ 01 11³ 10 1 2 00 01 11 10 12 8 4 5 7 6 13 9 15 W 14 X 11 10 N

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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### Educational Content #### Problem Statement: 1. **Objective:** Fill in the Karnaugh map for the given function and find the minimized Sum of Products (SOP) expression and the canonical sum. 2. **Function Given:** \[ F = \sum_{W,X,Y,Z}(4, 5, 8, 10, 13, 14, 15) + d(2, 9) \] 3. **Tasks:** - Find the minimum SOP expression for the function. - Find the canonical sum. #### Diagram Explanation: Karnaugh Map - **Structure:** - The Karnaugh map is a 4x4 grid representing all possible values for combinations of variables \(W, X, Y, Z\). - The variables are labeled with binary values at the top and side: - Across the top: \(WX\) with binary values \(00, 01, 11, 10\). - Along the side: \(YZ\) with binary values \(00, 01, 11, 10\). - **Entries:** - The grid cells represent the output for all combinations of inputs. - The cells labeled are indices where the function or don't-care conditions are true. #### Details: - **Minterms (Σ):** The function is true for indices 4, 5, 8, 10, 13, 14, and 15. - **Don't-care conditions (d):** The indices for these conditions are 2 and 9. The diagram should correlate visually with this explanation itself, ensuring learners can map indices correctly on a Karnaugh map. ### Solution Steps 1. **Filling the Karnaugh Map:** - Place 1s in the cells corresponding to the minterms (4, 5, 8, 10, 13, 14, 15). - Place Xs in the cells for don't-care conditions (2, 9). 2. **Finding the Minimum SOP:** - Group 1s and Xs to form the largest possible power-of-two rectangles. - Write down the simplified expression in terms of the variables \(W, X, Y, Z\) that are constant within these groups. 3. **Finding the Canonical Sum:** - Express the function as a sum of the minterm indices used in the operation (\
Transcribed Image Text:### Educational Content #### Problem Statement: 1. **Objective:** Fill in the Karnaugh map for the given function and find the minimized Sum of Products (SOP) expression and the canonical sum. 2. **Function Given:** \[ F = \sum_{W,X,Y,Z}(4, 5, 8, 10, 13, 14, 15) + d(2, 9) \] 3. **Tasks:** - Find the minimum SOP expression for the function. - Find the canonical sum. #### Diagram Explanation: Karnaugh Map - **Structure:** - The Karnaugh map is a 4x4 grid representing all possible values for combinations of variables \(W, X, Y, Z\). - The variables are labeled with binary values at the top and side: - Across the top: \(WX\) with binary values \(00, 01, 11, 10\). - Along the side: \(YZ\) with binary values \(00, 01, 11, 10\). - **Entries:** - The grid cells represent the output for all combinations of inputs. - The cells labeled are indices where the function or don't-care conditions are true. #### Details: - **Minterms (Σ):** The function is true for indices 4, 5, 8, 10, 13, 14, and 15. - **Don't-care conditions (d):** The indices for these conditions are 2 and 9. The diagram should correlate visually with this explanation itself, ensuring learners can map indices correctly on a Karnaugh map. ### Solution Steps 1. **Filling the Karnaugh Map:** - Place 1s in the cells corresponding to the minterms (4, 5, 8, 10, 13, 14, 15). - Place Xs in the cells for don't-care conditions (2, 9). 2. **Finding the Minimum SOP:** - Group 1s and Xs to form the largest possible power-of-two rectangles. - Write down the simplified expression in terms of the variables \(W, X, Y, Z\) that are constant within these groups. 3. **Finding the Canonical Sum:** - Express the function as a sum of the minterm indices used in the operation (\
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