With the following functions use a 4:1 multiplexer(mux) and minimum number of extra gates. Remember that to create the inverse of an input variable (i.e., A’, B’, etc.), you need to use an inverter. Hint:remember that you may need to try different variables on the select lines (i.e., A and B, or B and C, or A and C) to find the solution with the minimum number of extra gates.
Implement each of the functions from from the above question using a 2:1 multiplexer(mux) and a minimumnumber of extra gates. Hint:remember that you may need to try different variables (i.e., A or B or C) on the select line to find the solutionwith the minimum number of extra gates.
please explain in detail with a truth table as well as the schematics using a MUX.
Transcribed Image Text:### Boolean Algebra Expressions
The image contains three different Boolean algebra expressions which are used in digital logic design. These expressions can be applied to simplify logic circuits or to analyze logic functions.
**(a) Expression:**
\[ Y = A'B'C + ABC + BC' \]
- **A'B'C:** The logic circuit output is true when A is false, B is false, and C is true.
- **ABC:** The output is true when A, B, and C are all true.
- **BC':** The output is true when B is true and C is false.
**(b) Expression:**
\[ Y = A'B + AB'C' \]
- **A'B:** The output is true when A is false and B is true.
- **AB'C':** The output is true when A is true, B is false, and C is false.
**(c) Expression:**
\[ Y = A' + BC' \]
- **A':** The output is true when A is false.
- **BC':** The output is true when B is true and C is false.
Each expression represents a different logic gate configuration that can be used to design specific logic circuits for computational tasks. Understanding these expressions helps in optimizing digital circuits for better efficiency and performance.
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![### Boolean Algebra Expressions
The image contains three different Boolean algebra expressions which are used in digital logic design. These expressions can be applied to simplify logic circuits or to analyze logic functions.
**(a) Expression:**
\[ Y = A'B'C + ABC + BC' \]
- **A'B'C:** The logic circuit output is true when A is false, B is false, and C is true.
- **ABC:** The output is true when A, B, and C are all true.
- **BC':** The output is true when B is true and C is false.
**(b) Expression:**
\[ Y = A'B + AB'C' \]
- **A'B:** The output is true when A is false and B is true.
- **AB'C':** The output is true when A is true, B is false, and C is false.
**(c) Expression:**
\[ Y = A' + BC' \]
- **A':** The output is true when A is false.
- **BC':** The output is true when B is true and C is false.
Each expression represents a different logic gate configuration that can be used to design specific logic circuits for computational tasks. Understanding these expressions helps in optimizing digital circuits for better efficiency and performance.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe11a97ac-ffa8-4eaf-8332-77f2befa0e8c%2F43b6f277-959b-4213-9794-a52861408d4e%2Fn10hyap_processed.png&w=3840&q=75)
