The number of control lines in a multiplexer is 5, identify the MUX.
32 ∶ 1
Multiplexer Basics and Control Lines
A multiplexer, often abbreviated as 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 a particular input line is controlled by a set of control lines (also known as select lines).
The relationship between the number of control lines and the number of data input lines in a multiplexer is fundamental to its operation. If a multiplexer has 'n' control lines, it can select from $2^\text{n}$ unique input lines.
Control Lines and MUX Type Calculation
To identify the type of MUX based on the number of control lines, we use a simple formula:
- Let 'n' be the number of control lines.
- Let 'N' be the number of data input lines.
- The relationship is given by: $\text{N} = 2^\text{n}$
In this question, it is given that the number of control lines in the multiplexer is 5.
So, we have:
- Number of control lines (n) = 5
Now, we can calculate the number of data input lines (N):
$\text{N} = 2^\text{n} = 2^5$
Calculating $2^5$:
$2^5 = 2 \times 2 \times 2 \times 2 \times 2 = 32$
Therefore, the multiplexer has 32 data input lines. Since a multiplexer always has one output line, it is a 32 ∶ 1 MUX.
Option Analysis for MUX Identification
Let's evaluate the given options based on our calculation:
| Option | MUX Type | Calculated Control Lines (n) from $2^\text{n}$ inputs | Matches Given Control Lines (5)? |
|---|---|---|---|
| 1 | 16 ∶ 1 | Since $16 = 2^4$, n = 4 | No |
| 2 | 5 ∶ 1 | Not a standard $2^\text{n} : 1$ MUX configuration based on control lines. | No |
| 3 | 32 ∶ 1 | Since $32 = 2^5$, n = 5 | Yes |
| 4 | 64 ∶ 1 | Since $64 = 2^6$, n = 6 | No |
Based on the analysis, the MUX with 5 control lines is a 32 ∶ 1 MUX.
Important Questions from Multiplexer
Number of control lines required for 16 to 1 multiplexer is _____
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?
