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### Using a 3x8 Multiplexer for Boolean Expression Simplification

**Task Description:**

1. **Instruction**: Use a 3x8 multiplexer where a, b, and c are the multiplexer inputs.

2. **Boolean Expression**: \( X(a, b, c) = a + b + c' \)

In this task, you are required to utilize a 3x8 multiplexer, configured with inputs labeled as a, b, and c. The objective is to implement the given Boolean expression \( X(a, b, c) = a + b + c' \). This expression involves logical OR operations and the complement of c. 

### Explanation

- **Multiplexer (MUX)**: A digital switching device that selects one of many input signals and forwards the selected input into a single line. A 3x8 multiplexer uses 3 select lines to choose from 8 input lines.

- **Inputs**:
  - \( a \), \( b \): Direct inputs.
  - \( c' \): The complement (NOT operation) of the input \( c \).

- **Boolean Operations**:
  - \( + \): Represents the logical OR operation.
  - \( '\): Denotes the logical NOT operation, indicating complementation.

### Steps to Implement

1. **Configure Inputs**: Set a, b, and c as the select lines of the multiplexer.
2. **Generate Complement**: Use an inverter to find \( c' \).
3. **Connect Inputs**: 
   - Depending on the select lines' logic levels, route the respective combinations towards the single output line of the MUX.
4. **Output Expression**: The MUX should output the logic combination equal to \( a + b + c' \).

### Practical Use

This setup is ideal for simplifying logic circuits in digital electronics, enabling efficient computation and reduced complexity.
Transcribed Image Text:### Using a 3x8 Multiplexer for Boolean Expression Simplification **Task Description:** 1. **Instruction**: Use a 3x8 multiplexer where a, b, and c are the multiplexer inputs. 2. **Boolean Expression**: \( X(a, b, c) = a + b + c' \) In this task, you are required to utilize a 3x8 multiplexer, configured with inputs labeled as a, b, and c. The objective is to implement the given Boolean expression \( X(a, b, c) = a + b + c' \). This expression involves logical OR operations and the complement of c. ### Explanation - **Multiplexer (MUX)**: A digital switching device that selects one of many input signals and forwards the selected input into a single line. A 3x8 multiplexer uses 3 select lines to choose from 8 input lines. - **Inputs**: - \( a \), \( b \): Direct inputs. - \( c' \): The complement (NOT operation) of the input \( c \). - **Boolean Operations**: - \( + \): Represents the logical OR operation. - \( '\): Denotes the logical NOT operation, indicating complementation. ### Steps to Implement 1. **Configure Inputs**: Set a, b, and c as the select lines of the multiplexer. 2. **Generate Complement**: Use an inverter to find \( c' \). 3. **Connect Inputs**: - Depending on the select lines' logic levels, route the respective combinations towards the single output line of the MUX. 4. **Output Expression**: The MUX should output the logic combination equal to \( a + b + c' \). ### Practical Use This setup is ideal for simplifying logic circuits in digital electronics, enabling efficient computation and reduced complexity.
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The function at each output terminal of a decoder is a min term and the function is given is max term. To convert the given function into max term, calculate the dual of the given function:

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