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JDY D write the Boolean Expression and then simplify using Boolean Algebra. B ) Y(un-simplified) =) Y(simplified)

JDY D write the Boolean Expression and then simplify using Boolean Algebra. B ) Y(un-simplified) =) Y(simplified)

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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### Boolean Expression Simplification #### Diagram Explanation The diagram shows a combination of logic gates with four inputs labeled A, B, C, and D leading to an output labeled Y. The configuration of these gates is as follows: 1. **Inputs:** - A connects to an OR gate. - B connects to both this OR gate and an AND gate. - C connects to the other input of the AND gate. - D connects directly to the final OR gate. 2. **Logic Gates:** - The first logic gate is an OR gate that takes A and B as inputs. - The second logic gate is an AND gate taking B and C as inputs. - The outputs of these two gates feed into another OR gate. - Input D connects directly to the output OR gate. 3. **Output:** - The final OR gate combines the outputs of the first OR gate, the AND gate, and input D to produce the output Y. #### Task: - **Write the Boolean Expression:** Formulate the Boolean expression based on the logic diagram. - **Simplify the Boolean Expression:** Apply Boolean algebra rules to simplify the expression. #### Steps: a) **Y (Un-simplified)** - Write the expression using OR, AND, and the given input variables. b) **Y (Simplified)** - Simplify the expression obtained in part (a) using Boolean algebra. Use the space provided to write your answers for the unsimplified and simplified Boolean expressions.
Transcribed Image Text:### Boolean Expression Simplification #### Diagram Explanation The diagram shows a combination of logic gates with four inputs labeled A, B, C, and D leading to an output labeled Y. The configuration of these gates is as follows: 1. **Inputs:** - A connects to an OR gate. - B connects to both this OR gate and an AND gate. - C connects to the other input of the AND gate. - D connects directly to the final OR gate. 2. **Logic Gates:** - The first logic gate is an OR gate that takes A and B as inputs. - The second logic gate is an AND gate taking B and C as inputs. - The outputs of these two gates feed into another OR gate. - Input D connects directly to the output OR gate. 3. **Output:** - The final OR gate combines the outputs of the first OR gate, the AND gate, and input D to produce the output Y. #### Task: - **Write the Boolean Expression:** Formulate the Boolean expression based on the logic diagram. - **Simplify the Boolean Expression:** Apply Boolean algebra rules to simplify the expression. #### Steps: a) **Y (Un-simplified)** - Write the expression using OR, AND, and the given input variables. b) **Y (Simplified)** - Simplify the expression obtained in part (a) using Boolean algebra. Use the space provided to write your answers for the unsimplified and simplified Boolean expressions.
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