f(a, b, c, d, e) = m(1, 2, 5, 9, 16, 17, 21, 22, 29, 31) + D(0,3, 4, 6, 7, 10, 13, 18, 19, 20, 23, 24, 25, 26, 28, 30) (1) In this function, the minterm elements are m(1, 2,...) these are the truth table entries for which the function has logic value 1. The elements D(0, 3,...) indicate the don't care terms (for which the logic value of f is not important; you can assume the entry to be a 0 or a 1, as convenient. • Use a 5-variable Karnaugh maps to find a minimized SOP and POS expressions for function f in Equation (1). Draw an AND, OR, NOT gate circuit for your expression. Use only 2-input AND and OR gates. If your design requires gates with more than two inputs, change your design to use only 2-input gates. Map your design to chips: 7404 (NOT), 7408 (AND) and 7432 (OR).

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**Transcription and Explanation**

---

### Function Definition and Terms

The function \( f(a, b, c, d, e) \) is defined as:

\[
f(a, b, c, d, e) = \sum m(1, 2, 5, 9, 16, 17, 21, 22, 29, 31) + \sum D(0, 3, 4, 6, 7, 10, 13, 18, 19, 20, 23, 24, 25, 26, 28, 30)
\]

- **Minterm Elements**: \( m(1, 2, \ldots) \) are the truth table entries for which the function has logic value 1.
- **Don't Care Conditions**: \( D(0, 3, \ldots) \) indicate entries for which the logic value of \( f \) is not important. These can be assumed to be 0 or 1 as convenient.

### Instructional Tasks

- **Karnaugh Maps**:
  - Use a 5-variable Karnaugh map to find minimized Sum of Products (SOP) and Product of Sums (POS) expressions for the function \( f \).

- **Circuit Design**:
  - Design an AND, OR, NOT gate circuit for your expression. Use only 2-input AND and OR gates. If your design requires gates with more than two inputs, modify your design to use only 2-input gates.

- **Chip Mapping**:
  - Map your circuit design to the following chips:
    - **7404**: NOT gate
    - **7408**: AND gate
    - **7432**: OR gate

### Graphs or Diagrams

There are no specific graphs or diagrams included in the image, but there is a reference to using Karnaugh maps for simplifying logic expressions, which involves a grid used to visually simplify Boolean expressions by minimizing logic terms through grouping minterms and don't care conditions.

--- 

This transcription is designed to aid understanding on the specific steps needed to simplify and implement the given logic function using specific digital logic tools and methods.
Transcribed Image Text:**Transcription and Explanation** --- ### Function Definition and Terms The function \( f(a, b, c, d, e) \) is defined as: \[ f(a, b, c, d, e) = \sum m(1, 2, 5, 9, 16, 17, 21, 22, 29, 31) + \sum D(0, 3, 4, 6, 7, 10, 13, 18, 19, 20, 23, 24, 25, 26, 28, 30) \] - **Minterm Elements**: \( m(1, 2, \ldots) \) are the truth table entries for which the function has logic value 1. - **Don't Care Conditions**: \( D(0, 3, \ldots) \) indicate entries for which the logic value of \( f \) is not important. These can be assumed to be 0 or 1 as convenient. ### Instructional Tasks - **Karnaugh Maps**: - Use a 5-variable Karnaugh map to find minimized Sum of Products (SOP) and Product of Sums (POS) expressions for the function \( f \). - **Circuit Design**: - Design an AND, OR, NOT gate circuit for your expression. Use only 2-input AND and OR gates. If your design requires gates with more than two inputs, modify your design to use only 2-input gates. - **Chip Mapping**: - Map your circuit design to the following chips: - **7404**: NOT gate - **7408**: AND gate - **7432**: OR gate ### Graphs or Diagrams There are no specific graphs or diagrams included in the image, but there is a reference to using Karnaugh maps for simplifying logic expressions, which involves a grid used to visually simplify Boolean expressions by minimizing logic terms through grouping minterms and don't care conditions. --- This transcription is designed to aid understanding on the specific steps needed to simplify and implement the given logic function using specific digital logic tools and methods.
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