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Obtain the simplified Boolean expressions for output F and G in terms of the input variables in the circuit: D-

Obtain the simplified Boolean expressions for output F and G in terms of the input variables in the circuit: D-

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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### Problem 4-2 **Objective:** Obtain the simplified Boolean expressions for output \( F \) and \( G \) in terms of the input variables in the circuit. #### Circuit Description: - **Inputs:** \( A, B, C, \) and \( D \) - **Logic Gates:** 1. **NOT Gate:** Takes input \( A \) and outputs \( \overline{A} \). 2. **AND Gate 1:** Takes inputs \( B \) and \( C \) and outputs \( BC \). 3. **OR Gate:** Combines \( BC \) and \( \overline{A} \) to output \( BC + \overline{A} \). 4. **AND Gate 2:** Takes input \( D \) and outputs \( D \). 5. **AND Gate 3:** Combines outputs from the OR Gate and \( D \), output of this is connected as one of the inputs to AND Gate 5. 6. **AND Gate 4:** Takes inputs \(\overline{A}\) and \( D \) and outputs \(\overline{A}D \). 7. **AND Gate 5 (Output F):** Combines outputs of OR Gate and AND Gate 3 to produce output \( F \). 8. **AND Gate 6 (Output G):** Combines outputs from OR Gate and AND Gate 4 to produce output \( G \). The diagram illustrates logical operations proceeding through various combinations of AND, OR, and NOT gates, using the inputs \( A, B, C, \) and \( D \) to derive \( F \) and \( G \). The task involves analyzing the circuit to derive and simplify the Boolean expressions for \( F \) and \( G \) based on these operations.
Transcribed Image Text:### Problem 4-2 **Objective:** Obtain the simplified Boolean expressions for output \( F \) and \( G \) in terms of the input variables in the circuit. #### Circuit Description: - **Inputs:** \( A, B, C, \) and \( D \) - **Logic Gates:** 1. **NOT Gate:** Takes input \( A \) and outputs \( \overline{A} \). 2. **AND Gate 1:** Takes inputs \( B \) and \( C \) and outputs \( BC \). 3. **OR Gate:** Combines \( BC \) and \( \overline{A} \) to output \( BC + \overline{A} \). 4. **AND Gate 2:** Takes input \( D \) and outputs \( D \). 5. **AND Gate 3:** Combines outputs from the OR Gate and \( D \), output of this is connected as one of the inputs to AND Gate 5. 6. **AND Gate 4:** Takes inputs \(\overline{A}\) and \( D \) and outputs \(\overline{A}D \). 7. **AND Gate 5 (Output F):** Combines outputs of OR Gate and AND Gate 3 to produce output \( F \). 8. **AND Gate 6 (Output G):** Combines outputs from OR Gate and AND Gate 4 to produce output \( G \). The diagram illustrates logical operations proceeding through various combinations of AND, OR, and NOT gates, using the inputs \( A, B, C, \) and \( D \) to derive \( F \) and \( G \). The task involves analyzing the circuit to derive and simplify the Boolean expressions for \( F \) and \( G \) based on these operations.
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