Number of control lines required for 16 to 1 multiplexer is
4
Multiplexer Basics and Control Lines
A multiplexer (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 switch that can connect one of many input channels to a common output channel based on a control signal.
Role of Control (Select) Lines
The selection of which input line is connected to the output is determined by a set of control lines, also known as select lines. The number of select lines dictates how many input lines the multiplexer can handle.
Relationship Between Inputs and Select Lines
For a multiplexer with '$n$' select lines, it can manage '$2^n$' different input lines. Each unique combination of the '$n$' select lines corresponds to one of the '$2^n$' input lines being chosen.
Calculating Lines for a 16-to-1 Multiplexer
The question asks for the number of control lines needed for a 16-to-1 multiplexer. This means there are 16 input lines.
We need to find the number of select lines, let's call it '$n$', such that the number of possible input lines ($2^n$) equals 16.
The equation is:
$$2^n = 16$$
To solve for '$n$', we can think about the powers of 2:
- $2^1 = 2$
- $2^2 = 4$
- $2^3 = 8$
- $2^4 = 16$
From this, we can see that when '$n = 4$', the equation $2^4 = 16$ holds true.
Analyzing the Options
Let's check the given options based on our calculation:
- Option 1: 2 select lines. This would support $2^2 = 4$ inputs, not 16.
- Option 2: 3 select lines. This would support $2^3 = 8$ inputs, not 16.
- Option 3: 4 select lines. This supports $2^4 = 16$ inputs, which matches the requirement.
- Option 4: 16 select lines. This would support $2^{16}$ inputs, which is far more than needed and incorrect for determining the select lines.
Therefore, 4 control lines are required for a 16-to-1 multiplexer.
Important Questions from Multiplexer
________ is used to carry digital data on analog lines.
_______ is a device that combines a large number of low speed transmission lines into a high speed line.
Which of the following can be used as a parallel to series converter?
In a multiplexer, if there are 4 input lines and 1 output line, then number of selection lines will be:
Consider the digital circuit shown below with two input lines A and B, two select lines S0 and S1, and an output line Y. The blocks Q and M represent active high 2:4 decoder and 4-to-1 multiplexer, respectively. Out of 16 possible input combinations, the number of combinations that produce Y=1 is ____________. (answer in integer)
Note: One input combination is an instance of [A B S1 S0].
