How many select bits are used for the 4 1 MUX?
The Correct Answer and Explanation is:
A 4-to-1 multiplexer (MUX) requires 2 select bits.
Explanation:
A multiplexer is a combinational circuit that allows multiple input signals to be routed to a single output, based on the values of control or select lines. The number of select lines determines how many inputs can be selected. In the case of a 4-to-1 MUX, there are 4 data inputs (let’s call them ( I_0, I_1, I_2, I_3 )), and only one output.
To understand why 2 select lines are sufficient for a 4-to-1 MUX, we need to recognize that the number of select lines (denoted as ( S )) is related to the number of data inputs (denoted as ( N )) by the formula:
[
S = \log_2(N)
]
Where:
- ( N ) is the number of input lines.
- ( S ) is the number of select lines.
For a 4-to-1 MUX, there are 4 inputs, so we use:
[
S = \log_2(4) = 2
]
This means that 2 select lines are enough to select one of the 4 inputs. These select lines, typically labeled as ( S_0 ) and ( S_1 ), work as follows:
- When ( S_1S_0 = 00 ), the MUX routes input ( I_0 ) to the output.
- When ( S_1S_0 = 01 ), the MUX routes input ( I_1 ) to the output.
- When ( S_1S_0 = 10 ), the MUX routes input ( I_2 ) to the output.
- When ( S_1S_0 = 11 ), the MUX routes input ( I_3 ) to the output.
Thus, the 2 select lines provide 4 possible combinations (00, 01, 10, 11), each corresponding to one of the 4 input lines. This configuration allows the MUX to select one of the 4 inputs and direct it to the output. Therefore, a 4-to-1 multiplexer requires 2 select bits.