iree inputs and two outputs is shown below. the output functions after the OR gates, G1 and G2, and the final output functions F1 and F2? Hint: what is Xe0 and X ® 1? X Closed (connected) + Open (not connected) c C B BA A -F1 F2 *-I<

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### Problem Description

A Programmable Logic Array (PLA) with three inputs (A, B, C) and two outputs is shown. The task is to determine the output functions after the OR gates \( G_1 \) and \( G_2 \), as well as the final output functions \( F_1 \) and \( F_2 \).

**Hint:** Consider what the XOR (⊕) operation between X and 0, and X and 1, implies for the output functions.

### Diagram Explanation

#### Inputs:
- A, B, C: The primary inputs to the PLA.
- Each input also has its complement, represented as A', B', and C'.

#### Connections:
- The diagram uses crosses (X) to indicate a connection (closed) and pluses (+) for no connection (open).
  
#### Product Terms:
- Four AND gates generate product terms, labeled 1, 2, 3, and 4.

#### OR Gates:
- Two OR gates, \( G_1 \) and \( G_2 \), combine the product terms.
  
#### Outputs:
- \( F_1 \) and \( F_2 \): The final outputs are derived from the OR gate outputs.

### Detailed Circuit Analysis

1. **AND Gate Connections:**
    - Creates product terms from combinations of inputs and their complements.

2. **OR Gates Combinations:**
    - \( G_1 \) combines specific product terms to produce an intermediate result.
    - \( G_2 \) combines another set of product terms.

3. **Final Functions \( F_1 \) and \( F_2 \):**
    - Each of these functions is derived from the results of the OR gates, considering the XOR logic.

Let's specify what X ⊕ 0 and X ⊕ 1 signify:
- \( X \oplus 0 = X \): XOR with 0 leaves the input unchanged.
- \( X \oplus 1 = \overline{X} \): XOR with 1 inverts the input.

### Steps to Derive Output Functions

1. Identify connected input combinations for each AND gate.
2. Determine the logic captured by the OR gates \( G_1 \) and \( G_2 \).
3. Apply the XOR logic using the hint to finalize \( F_1 \) and \( F_2 \).

By analyzing this PLA configuration, one can
Transcribed Image Text:### Problem Description A Programmable Logic Array (PLA) with three inputs (A, B, C) and two outputs is shown. The task is to determine the output functions after the OR gates \( G_1 \) and \( G_2 \), as well as the final output functions \( F_1 \) and \( F_2 \). **Hint:** Consider what the XOR (⊕) operation between X and 0, and X and 1, implies for the output functions. ### Diagram Explanation #### Inputs: - A, B, C: The primary inputs to the PLA. - Each input also has its complement, represented as A', B', and C'. #### Connections: - The diagram uses crosses (X) to indicate a connection (closed) and pluses (+) for no connection (open). #### Product Terms: - Four AND gates generate product terms, labeled 1, 2, 3, and 4. #### OR Gates: - Two OR gates, \( G_1 \) and \( G_2 \), combine the product terms. #### Outputs: - \( F_1 \) and \( F_2 \): The final outputs are derived from the OR gate outputs. ### Detailed Circuit Analysis 1. **AND Gate Connections:** - Creates product terms from combinations of inputs and their complements. 2. **OR Gates Combinations:** - \( G_1 \) combines specific product terms to produce an intermediate result. - \( G_2 \) combines another set of product terms. 3. **Final Functions \( F_1 \) and \( F_2 \):** - Each of these functions is derived from the results of the OR gates, considering the XOR logic. Let's specify what X ⊕ 0 and X ⊕ 1 signify: - \( X \oplus 0 = X \): XOR with 0 leaves the input unchanged. - \( X \oplus 1 = \overline{X} \): XOR with 1 inverts the input. ### Steps to Derive Output Functions 1. Identify connected input combinations for each AND gate. 2. Determine the logic captured by the OR gates \( G_1 \) and \( G_2 \). 3. Apply the XOR logic using the hint to finalize \( F_1 \) and \( F_2 \). By analyzing this PLA configuration, one can
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