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5 The circuit below has a 2-to-4 decoder with active high outputs connected to a 4-to-1 MUX with an active low output.

5 The circuit below has a 2-to-4 decoder with active high outputs connected to a 4-to-1 MUX with an active low output.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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**Title:** Circuit Analysis of 2-to-4 Decoder with 4-to-1 Multiplexer **Description:** This exercise involves a circuit consisting of a 2-to-4 decoder with active high outputs connected to a 4-to-1 multiplexer (MUX) with an active low output. The goal is to derive logical expressions for the circuit output. --- **Circuit Components:** 1. **2-to-4 Decoder:** - **Inputs:** A, B - **Outputs:** Y₀, Y₁, Y₂, Y₃ - **Select Lines:** S₁ (connected to A), S₀ (connected to B) 2. **4-to-1 Multiplexer (MUX):** - **Inputs:** I₀, I₁, I₂, I₃ - **Select Lines:** S₀, S₁ (connected to Y₀, Y₁, Y₂, Y₃ outputs of the decoder) - **Additional Inputs:** C, D (connected to the select lines of the MUX) - **Output:** f 3. **Connections:** - The output of the decoder is connected to the inputs I₀, I₁, I₂, and I₃ of the MUX. **Tasks:** (a) Derive a minimum Sum of Products (SOP) or a minimum Product of Sums (POS) expression for the output, \( f(A, B, C, D) \). (b) Repeat part (a) and derive expressions assuming the decoder outputs are active low. --- **Analysis Notes:** - **2-to-4 Decoder Function:** The decoder activates one of its four outputs based on the binary value of inputs A and B. - **4-to-1 MUX Function:** The MUX selects one of its four data inputs based on the select lines and provides it to the output. Here, C and D are used as additional select inputs. For each task, consider the logic configurations: - **Active High:** Decoder outputs are high when selected. - **Active Low:** Decoder outputs are low when selected. Understanding the behavior of these components and logic states will lead to deriving the expressions required for each part.
Transcribed Image Text:**Title:** Circuit Analysis of 2-to-4 Decoder with 4-to-1 Multiplexer **Description:** This exercise involves a circuit consisting of a 2-to-4 decoder with active high outputs connected to a 4-to-1 multiplexer (MUX) with an active low output. The goal is to derive logical expressions for the circuit output. --- **Circuit Components:** 1. **2-to-4 Decoder:** - **Inputs:** A, B - **Outputs:** Y₀, Y₁, Y₂, Y₃ - **Select Lines:** S₁ (connected to A), S₀ (connected to B) 2. **4-to-1 Multiplexer (MUX):** - **Inputs:** I₀, I₁, I₂, I₃ - **Select Lines:** S₀, S₁ (connected to Y₀, Y₁, Y₂, Y₃ outputs of the decoder) - **Additional Inputs:** C, D (connected to the select lines of the MUX) - **Output:** f 3. **Connections:** - The output of the decoder is connected to the inputs I₀, I₁, I₂, and I₃ of the MUX. **Tasks:** (a) Derive a minimum Sum of Products (SOP) or a minimum Product of Sums (POS) expression for the output, \( f(A, B, C, D) \). (b) Repeat part (a) and derive expressions assuming the decoder outputs are active low. --- **Analysis Notes:** - **2-to-4 Decoder Function:** The decoder activates one of its four outputs based on the binary value of inputs A and B. - **4-to-1 MUX Function:** The MUX selects one of its four data inputs based on the select lines and provides it to the output. Here, C and D are used as additional select inputs. For each task, consider the logic configurations: - **Active High:** Decoder outputs are high when selected. - **Active Low:** Decoder outputs are low when selected. Understanding the behavior of these components and logic states will lead to deriving the expressions required for each part.
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