In a multiplexer, the number of input lines is ‘n’ and the number of select lines is ‘m’. Which of the following is correct?
2 m= n
Understanding Multiplexer Input and Select Lines
A multiplexer, often shortened to MUX, is a combinational logic circuit that selects one of several analog or digital input signals and forwards the selected input into a single output line. The selection of which input line to forward is controlled by a set of select lines (also known as control lines).
Let's consider the components mentioned in the question:
- Input Lines (n): These are the data inputs to the multiplexer. The multiplexer chooses one of these lines based on the value on the select lines.
- Select Lines (m): These lines determine which input line is selected. The combination of binary values on these lines acts as an address to pick one specific input.
Relationship Between Select Lines and Input Lines
The number of unique combinations that can be represented by 'm' select lines is $2^m$. Each of these unique combinations corresponds to the selection of one distinct input line. Therefore, a multiplexer with 'm' select lines can select from a maximum of $2^m$ input lines. If the number of input lines is 'n', then the relationship between 'n' and 'm' must be:
\( n = 2^m \)
This relationship means that for a given number of select lines (m), the multiplexer can handle $2^m$ input lines. For example:
- If m = 1 select line, it can have $2^1 = 2$ input lines (a 2-to-1 MUX).
- If m = 2 select lines, it can have $2^2 = 4$ input lines (a 4-to-1 MUX).
- If m = 3 select lines, it can have $2^3 = 8$ input lines (an 8-to-1 MUX).
- If m = 4 select lines, it can have $2^4 = 16$ input lines (a 16-to-1 MUX).
Analyzing the Options
We are given the relationship \(n = 2^m\). Let's compare this with the provided options:
- Option 1: \(2^m = n\). This matches the relationship we derived.
- Option 2: \(2m = n\). This suggests a linear relationship, which is incorrect for multiplexers.
- Option 3: \(2^n = m\). This reverses the roles of inputs and select lines and is incorrect.
- Option 4: \(2n = m\). This is also incorrect and does not represent the exponential relationship.
Based on the fundamental operation of a multiplexer, the number of input lines 'n' is equal to $2$ raised to the power of the number of select lines 'm'.
Conclusion
The correct relationship between the number of input lines 'n' and the number of select lines 'm' in a multiplexer is \(2^m = n\).
Revision Table: Multiplexer Relationship
| Component | Symbol | Description |
|---|---|---|
| Input Lines | n | Data inputs to be selected |
| Select Lines | m | Control lines to select an input |
| Output Lines | 1 | Single output line carrying selected input |
| Relationship | \(n = 2^m\) | Number of inputs determined by select lines |
Additional Information on Digital Multiplexers
Multiplexers are essential components in digital design. They are used for data selection, routing, and implementing logic functions. The size of a multiplexer is typically described as "n-to-1 MUX", where 'n' is the number of input lines. Knowing the number of input lines (n), you can find the number of select lines (m) using the formula \(m = \log_2(n)\).
For instance, an 8-to-1 MUX has n=8 inputs. The number of select lines is \(m = \log_2(8) = 3\). This confirms the relationship \(n = 2^m\), as $8 = 2^3$.
Important Questions from Multiplexer
The number of control lines in a multiplexer is 5, identify the MUX.
Number of control lines required for 16 to 1 multiplexer is _____
________ is used to carry digital data on analog lines.
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?
