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Suppose only one multiplexer and one inverter are allowed to be used to implement any Boolean function of n variables. What is the minimum size of the multiplexer needed?
- a)2n lines to 1 line
- b)2n + 1 lines to 1 line
- c)2n − 1 lines to 1 line
- d)2n − 2 lines to 1 line
Correct answer is option 'C'. Can you explain this answer?
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Suppose only one multiplexer and one inverter are allowed to be used t...
The minimum size of the multiplexer needed is 2^n lines to 1 line.
To see why, note that a multiplexer with n select lines can select one of 2^n input lines to output on a single output line. Therefore, we can represent any Boolean function of n variables as a truth table with 2^n rows, where each row corresponds to a unique combination of input variable values. We can then use the select lines of the multiplexer to choose the corresponding output value for each input combination.
However, we also need to account for the fact that we are only allowed to use one inverter. We can use the inverter to invert any one of the input variables, which effectively doubles the number of input combinations that we can represent. Therefore, we need a multiplexer with at least 2^n+1 input lines to be able to implement any Boolean function of n variables using only one multiplexer and one inverter.
To see why, note that a multiplexer with n select lines can select one of 2^n input lines to output on a single output line. Therefore, we can represent any Boolean function of n variables as a truth table with 2^n rows, where each row corresponds to a unique combination of input variable values. We can then use the select lines of the multiplexer to choose the corresponding output value for each input combination.
However, we also need to account for the fact that we are only allowed to use one inverter. We can use the inverter to invert any one of the input variables, which effectively doubles the number of input combinations that we can represent. Therefore, we need a multiplexer with at least 2^n+1 input lines to be able to implement any Boolean function of n variables using only one multiplexer and one inverter.
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Suppose only one multiplexer and one inverter are allowed to be used t...
To select 2n lines, we need a select function with n bits. Here, with n variables, we have (n - 1) select bits, hence 2n - 1 data lines. So, MUX has 2n - 1 lines 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 n variables. What is the minimum size of the multiplexer needed?a)2nlines to 1 lineb)2n + 1lines to 1 linec)2n − 1lines to 1 lined)2n − 2lines to 1 lineCorrect answer is option 'C'. Can you explain this answer?
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