Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN: 9780133923605
Author: Robert L. Boylestad
Publisher: PEARSON
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**Priority Encoder Truth Table and Boolean Expression Derivation**

**Objective:**
Formulate the truth table for an 8-to-3 priority encoder. Utilize \( w_7, w_6, w_5, w_4, w_3, w_2, w_1, w_0 \) as inputs and \( y_2, y_1, y_0, z \) as outputs. Derive the simplified Boolean expressions for \( y_2 \) and \( z \).

**Description:**

- **Inputs:** 
  - \( w_7 \) to \( w_0 \) are the input lines, each representing a unique priority level from highest (\( w_7 \)) to lowest (\( w_0 \)).

- **Outputs:**
  - \( y_2, y_1, y_0 \): These outputs represent the binary encoding of the highest priority active input line.
  - \( z \): This output indicates whether any input is active, functioning as an enable/disable status signal.

**Requirements:**

1. Construct the truth table that maps inputs \( w_7 \) to \( w_0 \) to outputs \( y_2, y_1, y_0, \) and \( z \).
2. Derive simplified Boolean expressions for \( y_2 \) and \( z \).

Use the given information to understand the priority encoding mechanism, focusing on generating correct logic expressions for the encoder's outputs based on the priority rules.
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Transcribed Image Text:**Priority Encoder Truth Table and Boolean Expression Derivation** **Objective:** Formulate the truth table for an 8-to-3 priority encoder. Utilize \( w_7, w_6, w_5, w_4, w_3, w_2, w_1, w_0 \) as inputs and \( y_2, y_1, y_0, z \) as outputs. Derive the simplified Boolean expressions for \( y_2 \) and \( z \). **Description:** - **Inputs:** - \( w_7 \) to \( w_0 \) are the input lines, each representing a unique priority level from highest (\( w_7 \)) to lowest (\( w_0 \)). - **Outputs:** - \( y_2, y_1, y_0 \): These outputs represent the binary encoding of the highest priority active input line. - \( z \): This output indicates whether any input is active, functioning as an enable/disable status signal. **Requirements:** 1. Construct the truth table that maps inputs \( w_7 \) to \( w_0 \) to outputs \( y_2, y_1, y_0, \) and \( z \). 2. Derive simplified Boolean expressions for \( y_2 \) and \( z \). Use the given information to understand the priority encoding mechanism, focusing on generating correct logic expressions for the encoder's outputs based on the priority rules.
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