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
The device which changes from serial data to parallel data is:
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
Which of the following statements are true?
A. Frequency division multiplexing technique can be handled by digital circuits.
B. Time division multiplexing technique can be handled by analog circuits
C. Wavelength division multiplexing technique is used with optical fiber for combining two signals.
D. Frequency division multiplexing technique can be applied when the bandwidth of a link is greater than the bandwidth of the signals to be transmitted.
Choose the correct answer from the options given below :
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?
A digital computer has a common bus system for 8 registers 16 bits each. How many multiplexers are required to implement common bus? What size of multiplexers is required?
