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If a, b, c are 3-input variables, then Boolean function y = ab + bc + ca represents:
A 3-input majority gate
A 3-input minority gate
Carry output of a full adder
Product circuit for a, b, and c
Which of the above statements are correct?
- a)Only 2 and 3
- b)Only 2 and 4
- c)Only 1 and 3
- d)Only 1 and 4
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
If a, b, c are 3-input variables, then Boolean function y = ab + bc +...
Explanation:
The Boolean function y = ab * bc * ca represents the product of three variables a, b, and c. Let's analyze the function and its representation step by step.
1. 3-input Majority Gate:
A majority gate is a logic gate that outputs the majority value of its inputs. In a 3-input majority gate, the output will be 1 if at least two of the inputs are 1. However, in the given function y = ab * bc * ca, the output will be 1 only if all three variables a, b, and c are 1. Therefore, the given function does not represent a 3-input majority gate.
2. 3-input Minority Gate:
A minority gate is a logic gate that outputs the minority value of its inputs. In a 3-input minority gate, the output will be 0 if at least two of the inputs are 1. In the given function y = ab * bc * ca, the output will be 0 if any two variables a, b, or c are 0. Therefore, the given function represents a 3-input minority gate.
3. Carry Output of a Full Adder:
A full adder is a digital circuit that performs addition of three inputs: A, B, and an input carry (Cin). It produces a sum (S) and a carry out (Cout). The carry output represents the carry generated when adding the three inputs. The given function y = ab * bc * ca does not represent the carry output of a full adder as it does not involve any addition operation.
4. Product Circuit for a, b, and c:
A product circuit is a logic circuit that outputs the product of its inputs. The given function y = ab * bc * ca represents the product of three variables a, b, and c. Hence, the given function represents a product circuit for a, b, and c.
Conclusion:
From the above analysis, we can conclude that the correct statements are:
- The given function represents a 3-input minority gate.
- The given function represents a product circuit for variables a, b, and c.
The Boolean function y = ab * bc * ca represents the product of three variables a, b, and c. Let's analyze the function and its representation step by step.
1. 3-input Majority Gate:
A majority gate is a logic gate that outputs the majority value of its inputs. In a 3-input majority gate, the output will be 1 if at least two of the inputs are 1. However, in the given function y = ab * bc * ca, the output will be 1 only if all three variables a, b, and c are 1. Therefore, the given function does not represent a 3-input majority gate.
2. 3-input Minority Gate:
A minority gate is a logic gate that outputs the minority value of its inputs. In a 3-input minority gate, the output will be 0 if at least two of the inputs are 1. In the given function y = ab * bc * ca, the output will be 0 if any two variables a, b, or c are 0. Therefore, the given function represents a 3-input minority gate.
3. Carry Output of a Full Adder:
A full adder is a digital circuit that performs addition of three inputs: A, B, and an input carry (Cin). It produces a sum (S) and a carry out (Cout). The carry output represents the carry generated when adding the three inputs. The given function y = ab * bc * ca does not represent the carry output of a full adder as it does not involve any addition operation.
4. Product Circuit for a, b, and c:
A product circuit is a logic circuit that outputs the product of its inputs. The given function y = ab * bc * ca represents the product of three variables a, b, and c. Hence, the given function represents a product circuit for a, b, and c.
Conclusion:
From the above analysis, we can conclude that the correct statements are:
- The given function represents a 3-input minority gate.
- The given function represents a product circuit for variables a, b, and c.
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Community Answer
If a, b, c are 3-input variables, then Boolean function y = ab + bc +...
In the given input combination, if the majority of inputs are 1, then the Boolean (SOP) function gives a majority gate. In the given 3-input a, b, c if at least two inputs are '1' then the Boolean function y = ab + bc + ca represents majority gate. Consider the truth table of full adder
By using K-map method, the carry output is obtained as follows:
Thus the given Boolean function represents carry o/p of a full adder.
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If a, b, c are 3-input variables, then Boolean function y = ab + bc + ca represents: A 3-input majority gate A 3-input minority gate Carry output of a full adder Product circuit for a, b, and c Which of the above statements are correct?a)Only 2 and 3b)Only 2 and 4c)Only 1 and 3d)Only 1 and 4Correct answer is option 'C'. Can you explain this answer?
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