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Implement the following Boolean function F, together with the don't- care conditions d. Use minimum number of NAND gates for your implementation. F(A,B,C,D) = II (8,9,11,12,15) d(A,B,C,D) = E(0,2,7,14, 13)

Implement the following Boolean function F, together with the don't- care conditions d. Use minimum number of NAND gates for your implementation. F(A,B,C,D) = II (8,9,11,12,15) d(A,B,C,D) = E(0,2,7,14, 13)

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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**Boolean Function Implementation Using NAND Gates** Objective: Implement the following Boolean function \( F \), together with the don't-care conditions \( d \). Use the minimum number of NAND gates for your implementation. ### Function Details: - **Function \( F(A, B, C, D) \):** - Product of Maxterms (Π) at positions: 8, 9, 11, 12, 15. - Representation: \( F(A, B, C, D) = \Pi (8, 9, 11, 12, 15) \) - **Don't-care conditions \( d(A, B, C, D) \):** - Sum of Minterms (Σ) at positions: 0, 2, 7, 14, 13. - Representation: \( d(A, B, C, D) = \Sigma(0, 2, 7, 14, 13) \) ### Implementation Strategy: To implement \( F \) using the minimum number of NAND gates, consider simplifying the expression using the don't-care conditions. By leveraging these conditions, it is possible to minimize the logic required, thus reducing the number of NAND gates needed. Focus on: - Creating a Karnaugh map to identify simplifications. - Grouping Minterms and Maxterms accordingly while considering don't-care conditions for further simplification. - Translating the simplified Boolean expression into a NAND-only circuit. This approach optimizes logic circuit design, crucial for efficient digital systems.
Transcribed Image Text:**Boolean Function Implementation Using NAND Gates** Objective: Implement the following Boolean function \( F \), together with the don't-care conditions \( d \). Use the minimum number of NAND gates for your implementation. ### Function Details: - **Function \( F(A, B, C, D) \):** - Product of Maxterms (Π) at positions: 8, 9, 11, 12, 15. - Representation: \( F(A, B, C, D) = \Pi (8, 9, 11, 12, 15) \) - **Don't-care conditions \( d(A, B, C, D) \):** - Sum of Minterms (Σ) at positions: 0, 2, 7, 14, 13. - Representation: \( d(A, B, C, D) = \Sigma(0, 2, 7, 14, 13) \) ### Implementation Strategy: To implement \( F \) using the minimum number of NAND gates, consider simplifying the expression using the don't-care conditions. By leveraging these conditions, it is possible to minimize the logic required, thus reducing the number of NAND gates needed. Focus on: - Creating a Karnaugh map to identify simplifications. - Grouping Minterms and Maxterms accordingly while considering don't-care conditions for further simplification. - Translating the simplified Boolean expression into a NAND-only circuit. This approach optimizes logic circuit design, crucial for efficient digital systems.
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