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F(A,B,C,D)= m(0,1,2,3,4,7,14) F(A,B,C) = Σ„(0,1,2,3) d) Show how to implement the function E using only NAND gates.

F(A,B,C,D)= m(0,1,2,3,4,7,14) F(A,B,C) = Σ„(0,1,2,3) d) Show how to implement the function E using only NAND gates.

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
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Please solve subpart D
**Exercise 3: Multiplexor Circuit Analysis** This exercise involves analyzing a multiplexor circuit and simplifying the logic function derived from it. Follow the steps below to understand the process: **a) Complete the K-map for the function F as implemented.** The K-map is a tool used to simplify Boolean functions. Below is the completed K-map for the function F: - **Variables AB (columns) and CD (rows):** - 00, 01, 11, 10 for both AB and CD. - **Map Entries:** | | AB: 00 | 01 | 11 | 10 | |----|--------|----|----|----| | CD 0 | 1 | 0 | 0 | 0 | | CD 1 | 1 | 1 | 1 | 0 | | CD 3 | 1 | 0 | 0 | 0 | | CD 2 | 1 | 0 | 0 | 0 | **b) Reduced 3-variable K-map (using D as the map-entered variable):** - **Variables A (rows) and BC (columns):** - 00, 01, 11, 10 for BC and 0, 1 for A. - **Map Entries:** | | BC: 00 | 01 | 11 | 10 | |----|--------|----|----|----| | A0 | 1 | 1 | 1 | 0 | | A1 | 0 | 0 | 0 | 0 | **c) Provide the minimum sum for the function F.** - The sum of products is minimized using the K-map simplification. - **Function Expressions:** - \( F(A, B, C, D) = \Sigma m(0, 1, 2, 3, 4, 7, 14) \) - \( F(A, B, C) = \Sigma m(0, 1, 2, 3) \) **d) Implement the function F using only NAND gates.** To implement the function F using only NAND gates, apply logic gate transformations.
Transcribed Image Text:**Exercise 3: Multiplexor Circuit Analysis** This exercise involves analyzing a multiplexor circuit and simplifying the logic function derived from it. Follow the steps below to understand the process: **a) Complete the K-map for the function F as implemented.** The K-map is a tool used to simplify Boolean functions. Below is the completed K-map for the function F: - **Variables AB (columns) and CD (rows):** - 00, 01, 11, 10 for both AB and CD. - **Map Entries:** | | AB: 00 | 01 | 11 | 10 | |----|--------|----|----|----| | CD 0 | 1 | 0 | 0 | 0 | | CD 1 | 1 | 1 | 1 | 0 | | CD 3 | 1 | 0 | 0 | 0 | | CD 2 | 1 | 0 | 0 | 0 | **b) Reduced 3-variable K-map (using D as the map-entered variable):** - **Variables A (rows) and BC (columns):** - 00, 01, 11, 10 for BC and 0, 1 for A. - **Map Entries:** | | BC: 00 | 01 | 11 | 10 | |----|--------|----|----|----| | A0 | 1 | 1 | 1 | 0 | | A1 | 0 | 0 | 0 | 0 | **c) Provide the minimum sum for the function F.** - The sum of products is minimized using the K-map simplification. - **Function Expressions:** - \( F(A, B, C, D) = \Sigma m(0, 1, 2, 3, 4, 7, 14) \) - \( F(A, B, C) = \Sigma m(0, 1, 2, 3) \) **d) Implement the function F using only NAND gates.** To implement the function F using only NAND gates, apply logic gate transformations.
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