Number of control lines required for 16 to 1 multiplexer is _____
4
Understanding Multiplexer Control Lines
A multiplexer (often abbreviated as MUX) is a digital circuit that selects one of several input signals and forwards it to a single output line. Think of it like a digital switchboard operator that connects one specific input line to the output based on selection commands.
Role of Control Lines
The selection process in a multiplexer is controlled by special input lines called control lines or select lines. The binary value applied to these select lines determines which specific input line is connected to the output.
Calculating the Number of Control Lines
For a multiplexer with N input lines, the number of select lines required, let's call it n, follows a specific relationship based on binary encoding. Each unique combination of the select lines corresponds to one input line. If there are n select lines, there are $2^n$ possible combinations of these lines.
Therefore, the number of input lines (N) must be equal to the number of possible combinations of the select lines ($2^n$):
$$ N = 2^n $$
In this specific question, we have a 16 to 1 multiplexer. This means there are 16 input lines (N = 16).
We need to find the number of control lines (n) required to select one out of these 16 inputs. Using the formula:
$$ 16 = 2^n $$
To solve for n, we can take the logarithm base 2 of both sides:
$$ n = \log_2(16) $$
We know that $2 \times 2 \times 2 \times 2 = 16$, which means $2^4 = 16$. So:
$$ n = 4 $$
Thus, 4 control lines are necessary to uniquely select any one of the 16 input lines for the multiplexer.
Conclusion
The number of control lines required for a 16 to 1 multiplexer is 4.
Important Questions from Multiplexer
The number of control lines in a multiplexer is 5, identify the MUX.
In a multiplexer, the number of input lines is ‘n’ and the number of select lines is ‘m’. Which of the following is correct?
________ is used to carry digital data on analog lines.
Consider a logic gate circuit. with 8 input lines (D 0, D 1..... D 7) and 3 output lines (A 0, A 1, A 2) specified by following operations
A 2= D 4+ D 5+ D 6+ D 7
A 1= D 2+ D 3+ D 6+ D 7
A 0= D 1+ D 3+ D 5+ D 0
Where + indicates logical OR operation. This circuit is
Consider the sentence below.
There is a country that borders both India and Pakistan.
Which of the following logical expressions express the above sentence correctly when the predicate Country(x) represents that x is a country and Borders(x, y) represents that the countries x and y share the border?
