Multiplexers (MUX) in Digital Logic: Selecting and Routing Data Signals
Understand multiplexers (MUX), combinational logic circuits used to select one of several input signals and direct it to a single output line. This guide explains multiplexer operation, their Boolean algebra representation, and their use in digital systems for data selection and routing.
Multiplexers in Digital Logic
What is a Multiplexer?
A multiplexer (MUX or mux), often called a data selector, is a combinational logic circuit that selects one of several input signals and forwards it to a single output line. The selection is controlled by a set of selection lines.
Multiplexer Structure
A 2n-to-1 multiplexer has 2n input data lines and n selection lines. The selection lines determine which input line is connected to the output. The output is a single line.
4x1 Multiplexer
(A block diagram of a 4x1 multiplexer should be included here. The four input lines (I₀-I₃), two selection lines (S₁, S₀), and single output line (y) should be clearly labeled.)
Truth Table for a 4x1 Multiplexer
| S₁ | S₀ | y |
|---|---|---|
| 0 | 0 | I₀ |
| 0 | 1 | I₁ |
| 1 | 0 | I₂ |
| 1 | 1 | I₃ |
Boolean Expression for a 4x1 Multiplexer
The Boolean expression for the output y is:
y = S₁'S₀'I₀ + S₁'S₀I₁ + S₁S₀'I₂ + S₁S₀I₃
(A circuit diagram showing the implementation of this Boolean expression using AND, OR, and NOT gates would be beneficial here.)
Building Larger Multiplexers
Larger multiplexers can be built using smaller multiplexers. For example, an 8x1 multiplexer can be constructed using two 4x1 multiplexers and one 2x1 multiplexer.
8x1 Multiplexer
(A block diagram of an 8x1 multiplexer constructed using two 4x1 multiplexers and a 2x1 multiplexer should be included here. The eight input lines (I₀-I₇), three selection lines (S₂, S₁, S₀), and the single output line (y) should be clearly labeled. The truth table for an 8x1 multiplexer should be included here.)
Conclusion
Multiplexers are essential components in digital systems for selecting one input from many inputs. Understanding their operation and design is crucial for a wide range of applications.