1. A combinational circuit is specified by the three Boolean functions: F(A, B, C) = C(A' + B') + AC' + BC' G(A, B, C) = ABC + BC H(A, B, C) = A + B a. b. C. Create a truth table for the circuit. Simplify the expressions using Karnaugh maps. Draw the logic diagram for the circuit using the simplified expressions obtained in part b.
1. A combinational circuit is specified by the three Boolean functions: F(A, B, C) = C(A' + B') + AC' + BC' G(A, B, C) = ABC + BC H(A, B, C) = A + B a. b. C. Create a truth table for the circuit. Simplify the expressions using Karnaugh maps. Draw the logic diagram for the circuit using the simplified expressions obtained in part b.
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![### Boolean Functions and Circuit Design
A combinational circuit is specified by the three Boolean functions:
\[ F(A, B, C) = C(A' + B') + AC' + BC' \]
\[ G(A, B, C) = ABC + BC \]
\[ H(A, B, C) = A \oplus B \]
#### Tasks:
**a. Create a truth table for the circuit.**
To create the truth table:
1. List all possible combinations of input values for \( A, B \), and \( C \).
2. Compute the values of the functions \( F, G \), and \( H \) for each combination of inputs.
**b. Simplify the expressions using Karnaugh maps.**
1. Plot the given Boolean expressions on Karnaugh maps.
2. Apply Karnaugh map simplification techniques to reduce the expressions.
**c. Draw the logic diagram for the circuit using the simplified expressions obtained in part b.**
1. Use the simplified Boolean expressions to draw the corresponding logic diagram.
2. Represent the logic gates (AND, OR, NOT, XOR) and their interconnections.
### Explanation of Terms:
- **Boolean Function:** A mathematical expression involving binary variables and logical operations such as AND, OR, NOT, and XOR.
- **Truth Table:** A table showing all possible input values and the corresponding output for a Boolean function.
- **Karnaugh Map (K-Map):** A diagram used in Boolean algebra to simplify expressions. It is a visual method for minimizing the number of logical operations.
- **Logic Diagram:** A graphical representation of a circuit that shows the arrangement of logic gates and their interconnections.
By completing these tasks, we derive optimal logic gate implementations of the given Boolean functions, facilitating the design of efficient combinational circuits.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5646b139-543d-4164-b214-191929b49dde%2F1dd9774d-f791-4123-a5f3-a59c1460d359%2Fba4pnwj_processed.png&w=3840&q=75)
Transcribed Image Text:### Boolean Functions and Circuit Design
A combinational circuit is specified by the three Boolean functions:
\[ F(A, B, C) = C(A' + B') + AC' + BC' \]
\[ G(A, B, C) = ABC + BC \]
\[ H(A, B, C) = A \oplus B \]
#### Tasks:
**a. Create a truth table for the circuit.**
To create the truth table:
1. List all possible combinations of input values for \( A, B \), and \( C \).
2. Compute the values of the functions \( F, G \), and \( H \) for each combination of inputs.
**b. Simplify the expressions using Karnaugh maps.**
1. Plot the given Boolean expressions on Karnaugh maps.
2. Apply Karnaugh map simplification techniques to reduce the expressions.
**c. Draw the logic diagram for the circuit using the simplified expressions obtained in part b.**
1. Use the simplified Boolean expressions to draw the corresponding logic diagram.
2. Represent the logic gates (AND, OR, NOT, XOR) and their interconnections.
### Explanation of Terms:
- **Boolean Function:** A mathematical expression involving binary variables and logical operations such as AND, OR, NOT, and XOR.
- **Truth Table:** A table showing all possible input values and the corresponding output for a Boolean function.
- **Karnaugh Map (K-Map):** A diagram used in Boolean algebra to simplify expressions. It is a visual method for minimizing the number of logical operations.
- **Logic Diagram:** A graphical representation of a circuit that shows the arrangement of logic gates and their interconnections.
By completing these tasks, we derive optimal logic gate implementations of the given Boolean functions, facilitating the design of efficient combinational circuits.
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