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Suppose only one multiplexer and one inverter are allowed to be used to implement any Boolean function of variables.
What is the minimum size of the multiplexer needed?
What is the minimum size of the multiplexer needed?
- a)2n line to 1 line
- b)2n + 1 line to 1 line
- c)2n - 1 line to 1 line
- d)2n - 2 line to 1 line
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Suppose only one multiplexer and one inverter are allowed to be used t...
2n - 1
We will map variables to select lines and variable to input line
We will map variables to select lines and variable to input line
Most Upvoted Answer
Suppose only one multiplexer and one inverter are allowed to be used t...
The minimum size of the multiplexer needed to implement any Boolean function of variables using only one multiplexer and one inverter is 2n - 1 line to 1 line.
Explanation:
A multiplexer is a combinational circuit that selects one of many inputs and forwards it to a single output. It has two sets of inputs - data inputs and select inputs. The select inputs determine which data input is selected and forwarded to the output.
In this scenario, we are allowed to use only one multiplexer and one inverter to implement any Boolean function of variables. This means we need to find the minimum size of the multiplexer that can handle any Boolean function.
Let's consider the Boolean function of n variables, f(x1, x2, ..., xn).
1. Inverter:
An inverter simply takes an input and produces its complement. So, we can use the inverter to complement any input variable.
2. Multiplexer:
We can use the multiplexer to implement a function of n-1 variables. The select inputs of the multiplexer can be used to determine which n-1 variables are considered for the function.
For example, let's consider the Boolean function of 2 variables, f(x1, x2). We can implement this function using a 2-line to 1-line multiplexer.
- The inputs x1 and x2 are connected to the data inputs of the multiplexer.
- The select input of the multiplexer is connected to the inverter of x1.
- The output of the multiplexer is the output of the Boolean function.
The select input determines which input variable is selected based on its complement. If the select input is 0 (x1 is complemented), then x2 is selected. If the select input is 1 (x1 is not complemented), then x1 is selected.
This approach can be extended to any number of variables. For n variables, we need a multiplexer with 2n-1 data inputs and n select inputs.
Therefore, the minimum size of the multiplexer needed to implement any Boolean function of variables using only one multiplexer and one inverter is 2n - 1 line to 1 line.
Explanation:
A multiplexer is a combinational circuit that selects one of many inputs and forwards it to a single output. It has two sets of inputs - data inputs and select inputs. The select inputs determine which data input is selected and forwarded to the output.
In this scenario, we are allowed to use only one multiplexer and one inverter to implement any Boolean function of variables. This means we need to find the minimum size of the multiplexer that can handle any Boolean function.
Let's consider the Boolean function of n variables, f(x1, x2, ..., xn).
1. Inverter:
An inverter simply takes an input and produces its complement. So, we can use the inverter to complement any input variable.
2. Multiplexer:
We can use the multiplexer to implement a function of n-1 variables. The select inputs of the multiplexer can be used to determine which n-1 variables are considered for the function.
For example, let's consider the Boolean function of 2 variables, f(x1, x2). We can implement this function using a 2-line to 1-line multiplexer.
- The inputs x1 and x2 are connected to the data inputs of the multiplexer.
- The select input of the multiplexer is connected to the inverter of x1.
- The output of the multiplexer is the output of the Boolean function.
The select input determines which input variable is selected based on its complement. If the select input is 0 (x1 is complemented), then x2 is selected. If the select input is 1 (x1 is not complemented), then x1 is selected.
This approach can be extended to any number of variables. For n variables, we need a multiplexer with 2n-1 data inputs and n select inputs.
Therefore, the minimum size of the multiplexer needed to implement any Boolean function of variables using only one multiplexer and one inverter is 2n - 1 line to 1 line.
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Suppose only one multiplexer and one inverter are allowed to be used to implement any Boolean function of variables.What is the minimum size of the multiplexer needed?a)2nline to 1 lineb)2n +1line to 1 linec)2n - 1line to 1 lined)2n - 2 line to 1 lineCorrect answer is option 'C'. Can you explain this answer?
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