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5. AB+ CD = X D K AB D CD -U с AB+CD

5. AB+ CD = X D K AB D CD -U с AB+CD

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Please do truth table #5
## Logic Gate Diagrams and Boolean Expressions ### 1. NOT Gate This section explains the NOT gate, which inverts the input signal. The output of the NOT gate is denoted as \(X\), where: \[ X = \overline{A} \] - **Diagram:** A single input \(A\) going through a NOT gate, producing an output \( \overline{A} \). ### 2. AND Gate The AND gate outputs \(1\) only when all inputs are \(1\). In this context: \[ ABC = X \] - **Diagram:** Three inputs labeled \(A\), \(B\), and \(C\) enter an AND gate. The output is labeled \(ABC\). ### 3. OR Gate An OR gate outputs \(1\) when at least one input is \(1\). The expression given is: \[ AB + CD = X \] - **Diagram:** There are two AND gates and one OR gate contributing to the output \(X\). Inputs \(A\) and \(B\) are connected to the first AND gate, while inputs \(C\) and \(D\) are connected to the second AND gate. The outputs of both AND gates are inputs to the OR gate. ### 4. Complex Logic Gate Combination This section elaborates on a more complex combination of logic gates: \[ AB + \overline{A} = X \] - **Diagram:** An AND gate with inputs \(A\) and \(B\) produces \(AB\). A NOT gate inverts \(A\) to produce \( \overline{A} \). Finally, an OR gate combines \(AB\) and \(\overline{A} \) to produce \(X\). ### Diagram Description: 1. **NOT Gate**: Simple diagram with input \(A\) leading to a NOT gate and output \( \overline{A} \). 2. **AND Gate**: Inputs \(A\), \(B\), and \(C\) are connected to an AND gate producing output \(ABC\). 3. **OR Gate**: Two AND gates with inputs \(A, B\) and \(C, D\) feeding into an OR gate, resulting in \(X = AB + CD\). 4. **Combination Logic**: An AND gate processes \(A\) and \(B\) inputs (output \(
Transcribed Image Text:## Logic Gate Diagrams and Boolean Expressions ### 1. NOT Gate This section explains the NOT gate, which inverts the input signal. The output of the NOT gate is denoted as \(X\), where: \[ X = \overline{A} \] - **Diagram:** A single input \(A\) going through a NOT gate, producing an output \( \overline{A} \). ### 2. AND Gate The AND gate outputs \(1\) only when all inputs are \(1\). In this context: \[ ABC = X \] - **Diagram:** Three inputs labeled \(A\), \(B\), and \(C\) enter an AND gate. The output is labeled \(ABC\). ### 3. OR Gate An OR gate outputs \(1\) when at least one input is \(1\). The expression given is: \[ AB + CD = X \] - **Diagram:** There are two AND gates and one OR gate contributing to the output \(X\). Inputs \(A\) and \(B\) are connected to the first AND gate, while inputs \(C\) and \(D\) are connected to the second AND gate. The outputs of both AND gates are inputs to the OR gate. ### 4. Complex Logic Gate Combination This section elaborates on a more complex combination of logic gates: \[ AB + \overline{A} = X \] - **Diagram:** An AND gate with inputs \(A\) and \(B\) produces \(AB\). A NOT gate inverts \(A\) to produce \( \overline{A} \). Finally, an OR gate combines \(AB\) and \(\overline{A} \) to produce \(X\). ### Diagram Description: 1. **NOT Gate**: Simple diagram with input \(A\) leading to a NOT gate and output \( \overline{A} \). 2. **AND Gate**: Inputs \(A\), \(B\), and \(C\) are connected to an AND gate producing output \(ABC\). 3. **OR Gate**: Two AND gates with inputs \(A, B\) and \(C, D\) feeding into an OR gate, resulting in \(X = AB + CD\). 4. **Combination Logic**: An AND gate processes \(A\) and \(B\) inputs (output \(
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