Design, build, Karnaugh map and Equations to verify the logic circuit described by; a) f(a,b,c,d) = Em(0, 1, 3, 7, 8, 9, 10, 14) Where d is LSb (least-significant bit) and a is MSb (most-significant bit) using a minimal sum of products (SOP) implementation. Assign the output f to LD0 and the inputs a through d to SW3 through SW0 b) fla,b.c.d) = Em(0, 4, 6, 7, 11, 14, 15) Where d is LSb (least-significant bit) and a is MSb (most-significant bit) using a minimal sum of products (SOP) implementation. Assign the output f to LD0 and the inputs a through d to SW3 through SW0

Database System Concepts
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Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
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Chapter1: Introduction
Section: Chapter Questions
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**Design and Verification of Logic Circuits Using Karnaugh Maps and SOP Implementation**

In this educational exercise, two logic circuits are described and need to be confirmed through designing and building Karnaugh maps and deriving equations.

---

**Task Overview:**

For each logic circuit, the goal is to:

1. Design Karnaugh maps.
2. Use these maps to derive minimal Sum of Products (SOP) equations.
3. Verify the design through implementation.

---

**Exercise a:**

- **Function to Verify:**
  \[
  f(a, b, c, d) = \Sigma m(0, 1, 3, 7, 8, 9, 10, 14)
  \]

- **Bit Representation:**
  - \(d\) is the LSB (least-significant bit).
  - \(a\) is the MSB (most-significant bit).

- **Implementation:**
  Use the minimal SOP method.

- **Assignments:**
  - Assign output \(f\) to \(LD0\).
  - Assign inputs \(a\) through \(d\) to \(SW3\) through \(SW0\).

---

**Exercise b:**

- **Function to Verify:**
  \[
  f(a, b, c, d) = \Sigma m(0, 4, 6, 7, 11, 14, 15)
  \]

- **Bit Representation:**
  - \(d\) is the LSB (least-significant bit).
  - \(a\) is the MSB (most-significant bit).

- **Implementation:**
  Use the minimal SOP method.

- **Assignments:**
  - Assign output \(f\) to \(LD0\).
  - Assign inputs \(a\) through \(d\) to \(SW3\) through \(SW0\).

By following this structured approach, learners will be able to visualize and implement logical expressions effectively, aiding their understanding of digital logic design principles.
Transcribed Image Text:**Design and Verification of Logic Circuits Using Karnaugh Maps and SOP Implementation** In this educational exercise, two logic circuits are described and need to be confirmed through designing and building Karnaugh maps and deriving equations. --- **Task Overview:** For each logic circuit, the goal is to: 1. Design Karnaugh maps. 2. Use these maps to derive minimal Sum of Products (SOP) equations. 3. Verify the design through implementation. --- **Exercise a:** - **Function to Verify:** \[ f(a, b, c, d) = \Sigma m(0, 1, 3, 7, 8, 9, 10, 14) \] - **Bit Representation:** - \(d\) is the LSB (least-significant bit). - \(a\) is the MSB (most-significant bit). - **Implementation:** Use the minimal SOP method. - **Assignments:** - Assign output \(f\) to \(LD0\). - Assign inputs \(a\) through \(d\) to \(SW3\) through \(SW0\). --- **Exercise b:** - **Function to Verify:** \[ f(a, b, c, d) = \Sigma m(0, 4, 6, 7, 11, 14, 15) \] - **Bit Representation:** - \(d\) is the LSB (least-significant bit). - \(a\) is the MSB (most-significant bit). - **Implementation:** Use the minimal SOP method. - **Assignments:** - Assign output \(f\) to \(LD0\). - Assign inputs \(a\) through \(d\) to \(SW3\) through \(SW0\). By following this structured approach, learners will be able to visualize and implement logical expressions effectively, aiding their understanding of digital logic design principles.
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