A multiplexer (MUX) is a digital electronic device that allows multiple input signals to be selected and routed to a single output line. It operates based on the control signals applied to its select lines, which determine which input data is chosen and transmitted to the output. MUX is widely used in various digital systems for data selection and routing purposes.
A basic MUX has the following components:
Input lines (n): These are the data input lines where different data sources are connected. A multiplexer can have 2^n input lines, meaning it can select one of 2^n input sources to be transmitted to the output.
Output line: This is the single line where the selected data from the input lines is transmitted.
Select lines (log2(n)): These are the control lines used to select which input line's data will be passed to the output. The number of select lines depends on the number of input lines (n). For example, if there are 4 input lines, there will be 2 select lines (log2(4) = 2).
The operation of a multiplexer can be explained using a truth table and logic expressions. For an n-input MUX, the truth table will have 2^n rows, where each row corresponds to a specific combination of select line values (0 or 1).
Let's take an example of a 2-to-1 MUX, which has two input lines (n = 2) and one output line. It has 2 select lines (log2(2) = 1).
Select (S) Input 1 (I0) Input 2 (I1) Output (Y)
0 D0 D1 Y = D0
1 D2 D3 Y = D3
The logic expression for the output (Y) of the 2-to-1 MUX can be written as:
Y = S' * I0 + S * I1
In this expression, S' represents the complement of the select line (when S is 0, S' is 1, and vice versa). The multiplexer selects either I0 or I1 based on the value of the select line S.
When S is 0 (S' is 1), the output Y will be equal to I0, and when S is 1 (S' is 0), the output Y will be equal to I1. This way, the MUX can select one of the two inputs and route it to the output based on the control signal provided by the select line.
The operation of MUXes with more input lines follows the same principle but requires a larger truth table and more complex logic expressions. However, the fundamental concept remains the same: a MUX selects one input line from many and forwards its data to the output line based on the control signals applied to its select lines.